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This paper aims to study the modified Gardner (mG) equation that was proposed in the literature a short while ago. We first construct conserved vectors of the mG equation by invoking three different techniques; namely the method of multiplier, Noether’s theorem, and the conservation theorem owing to Ibragimov. Thereafter, we present exact solutions to the mG equation by invoking a complete discrimination system for the fifth degree polynomial. Finally, we simulate collisions of solitons for the mG equation.

Higher-order nonlinear wave models have been a source of attraction to a huge number of researchers in recent times as a result of their significance in mathematical physics, other nonlinear sciences as well as engineering. In consequence, we outline in this paper the analytical studies entrenched on a generalized structure of a nonlinear breaking soliton equation with higher-order nonlinearity in four variables which have applications in science as well as engineering. Lie group theory is utilized to generate an 11-dimensional Lie algebra associated with the equation under consideration and in addition one parametric group of transformations related to the algebra is calculated. Besides, the technique is further invoked in performing reductions of the various subalgebras of the understudy model. Moreover, in conjunction with the theory, the direct integration technique is engaged to secure an analytic solution of the equation and as a result, a general analytic solution with regard to the second-kind elliptic-integral function is furnished. Moreover, we engage the novel simplest equation technique to gain more general solutions to the equation. In consequence, solitonic solutions comprising periodic, dark-bright, topological kink as well as singular solutions are achieved. We complemented that by exhibiting the dynamics of the secured solutions with the aid of graphical representations. In conclusion, we calculate conserved quantities associated with the aforementioned equation by invoking the well-celebrated classical Noether theorem technique.

In this study, we investigate the travelling wave solutions of the (2+1)-dimensional new generalized Korteweg–de Vries equation by employing Lie group analysis along with various techniques which include direct integration, simplest equation method and Kudryashov’s method. The results obtained consists of periodic, kink, soliton and hyperbolic solutions. The symbolic computation software Maple is used to check the accuracy of all solutions obtained. Finally, 3D, density, and 2D plots of the derived solution are displayed to show the physical appearance of the model. Furthermore, we utilize the general multiplier technique and Ibragimov’s method to derive its conserved vectors. Conservation of energy and momentum, amongst others were found. Conservation laws have many significant uses with regards to integrability, linearization and analysis of solutions.

Solow Growth Model (SGM) is an economic model that is exogenous in nature and examines the relationship between the output and input levels in an economy over a period of time. It projects long-term economic growth in relation to labour (population growth), savings rate, and technological development. However, traditional approaches to solving the Solow growth model may rely on complex mathematical techniques that might not give an accurate representation of real-world economic dynamics. Thus, this paper applies the Natural Decomposition Method (NDM) to the Solow growth financial model. The NDM is a numerical technique that combines the Natural Transform (NT) and the ADM-Adomian decomposition method. The NDM simplifies problem-solving by converting the original differential equations into algebraic equations as regards limitations associated with nonlinear models. From the results obtained by applying the NDM to the Solow growth financial model, researchers and policymakers can better understand the interplay between financial variables, such as savings rates, investment, and capital allocation, and their impact on economic growth dynamics, as a systematic approach to capturing the complex relationship between finance and economic development within the Solow framework is ensured. Further research and application of the NDM can contribute to advancing the knowledge of economic dynamics and support evidence-based decision-making in economic policy.

In this investigation, we explore the mathematical intricacies of the novel (2+1)-dimensional Bogoyavlensky-Konopelchenko equation, a model with practical applications in elucidating the dynamics of internal waves within deep water. The equation’s significance spans various scientific domains, including plasma physics, nonlinear optics, and fluid dynamics. Employing a comprehensive analytical approach, specifically Lie symmetry analysis, we aim to unravel the underlying complexities of this equation and obtain new analytical solutions. To further scrutinize the equation, we apply various methods, namely Kudryashov’s method, the (G′/G)-expansion method, the simplest equation technique, and the power series method, all of which have not been applied to the equation before. Through these techniques, we successfully derive solutions in diverse functional forms, encompassing rational, trigonometric, exponential, hyperbolic, and Jacobi elliptic functions. To enhance comprehension, we present our findings visually using three-dimensional and two-dimensional plots density plots via the Mathematica tool. These graphical representations effectively communicate the intricate characteristics and nuances inherent in the solutions. Our visual representations reveal a spectrum of patterns, including periodic, singular periodic, kink-shaped structures. Additionally, our investigation extends to the determination of conserved quantities associated with the new (2+1)-dimensional Bogoyavlensky-Konopelchenko equation. This involves the application of the multiplier method and Ibragimov’s theorem, two potent techniques for identifying and understanding the conservation laws governing the model.

This work delves into the analysis of the Gilson–Pickering equation which governs the waves propagation in plasma physics by invoking Lie symmetry analysis. We commence by identifying the Lie point symmetries associated with the equation. These symmetries are then leveraged on to compute the commutator table and subsequently the adjoint representation, ultimately leading to the establishment of an optimal system of one-dimensional subalgebras. Each subalgebra within this system is subsequently utilized to perform symmetry reductions. Through these reductions, various forms of nonlinear ordinary differential equations are obtained, which are subsequently solved using the power series method and Kudryashov’s technique. The resulting solutions are given in terms of hyperbolic functions. To gain deeper insights into the behaviour of these solutions, three-dimensional and two-dimensional plots are presented. Furthermore, applying the Ibragimov’s theorem allows us to derive conserved vectors associated with the Gilson–Pickering equation.

In this paper, we study the Camassa–Holm type equation, which has applications in mathematical physics and engineering. Its applications extend across disciplines, contributing to our understanding of complex systems and helping to develop innovative solutions in diverse areas of research. Our main aim is to construct closed-form solutions of the equation using a powerful technique, namely the Lie group analysis method. Firstly, we derive the Lie point symmetries of the equation. Thereafter, the equation is reduced to non-linear ordinary differential equations using symmetry reductions. Furthermore, the solutions of the equation are derived using the extended Jacobi elliptic function technique, the simplest equation method, and the power series method. In conclusion, we construct conservation laws for the equation using Noether’s theorem and the multiplier approach, which plays a crucial role in understanding the behavior of non-linear equations, especially in physics and engineering, and these laws are derived from fundamental principles such as the conservation of mass, energy, momentum, and angular momentum.

This article investigates a new generalized two-dimensional nonlinear wave equation of engineering physics with various applications in the fields of sciences and engineering. In this study, shock wave and solitary wave solutions were secured via the sine–Gordon technique. Moreover, various new group invariants along-side exact classical results of the equation were achieved through the utilization of Lie group theoretic techniques. Some of the solutions are gained with regards to Weierstrass functions, complex soliton, topological kink soliton as well as singular soliton. Besides, several algebraic and other solitary-wave-type solutions are obtained. Wave dynamics of the solutions are plotted to give more physical meanings to the obtained results and have a better knowledge of what the nonlinear wave equation represents in terms of physical phenomena. Application of the secured results in engineering (signal processing), physics (electromagnetism) and complex media are presented.

Deposit insurance is a mechanism by which financial institutions are stabilized. The danger of a bank’s inability to meet its consumer commitments due to its suspended license is insured through deposit insurance practices. A flat-rate insurance scheme would contribute to moral hazard and a financial panic when banks indulge in dangerous practices. Hence, a reliable model with an explicit solution is required. This paper considers a risk rate model for deposit insurance engendered by the classical Black Scholes Option Pricing Model. The solutions are obtained via the application of Banach Contraction Mapping or Method. The procedures involved are straightforward, easy, and flexible, even without giving up accuracy. The desired explicit solutions are obtained with less computational time.

This paper presents analytical studies carried out explicitly on a higher-dimensional generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity arising in engineering and nonlinear science. We obtain analytic solutions for the underlying equation via Lie group approach as well as direct integration method. Moreover, we engage the extended Jacobi elliptic cosine and sine amplitude functions expansion technique to seek more exact travelling wave solutions of the equation for some particular cases. Consequently, we secure, singular and nonsingular (periodic) soliton solutions, cnoidal, snoidal as well as dnoidal wave solutions. Besides, we depict the dynamics of the solutions using suitable graphs. The application of obtained results in various fields of sciences and engineering are presented. In conclusion, we construct conserved currents of the aforementioned equation via Noether’s theorem (with Helmholtz criteria) and standard multiplier technique through the homotopy formula.

Nonlinear partial differential equations emerge in an extensive variants of physical problems inclusive of fluid dynamics, solid mechanics, plasma physics, quantum field theory as well as mathematics and engineering. It has also been noticed that systems of nonlinear partial differential equations arise in biological and chemical applications. This article presents the analytical investigation of a completely generalized (3 + 1)-dimensional nonlinear potential Yu-Toda-Sasa-Fukuyama equation which has applications in the fields of engineering and physics. The generalized version of the potential Yu-Toda-Sasa-Fukuyama equation is more comprehensively studied in this paper compared to other research work previously done on the equation, with various new solutions of interests achieved. The theory of Lie group is applied to the nonlinear partial differential equation to basically reduce the equation to an integrable form which consequently allows for direct integration of the result. The rigorous process involved in performing a comprehensive reduction of the model under consideration using its Lie algebra makes it possible to achieve various nontrivial solutions. Besides, more general solutions are found via a well-known standard technique. In consequence, we secured diverse solitons and solutions of great interest including topological kink solitons, singular solitons, algebraic functions, exponential function, rational function, Weierstrass function, Jacobi elliptic function as well as series solutions of the underlying equation. Moreover, the completeness of the result was ascertained by presenting the solutions graphically. In addition, discussions of the pictorial representations of the results are done. Conclusively, we constructed conserved quantities of the underlying equation via both the variational and non-variational approaches using the classical Noether’s theorem as well as the standard multiplier technique respectively. In addition, some pertinent observations made from the secured results via both techniques are analyzed.

This work presents a generalized hyper-elastic rod wave (gHRW) equation from the Lie symmetry method’s standpoint. The equation illustrates dispersive waves generating in hyper-elastic rods. Using multiplier approach we find conserved vectors of the underlying equation. We subsequently obtain first integrals of the conserved vectors under the time–space group invariant u(t,x)=H(x−νt). Finally, by analysing various attainable instances of the arbitrary coefficient function g(u), we perform symmetry reductions of gHRW equation to lower order ordinary differential equations and in some instances obtain analytic solutions for special values of arbitrary constants.

In physics as well as mathematics, nonlinear partial differential equations are known as veritable tools in describing many diverse physical systems, ranging from gravitation, mechanics, fluid dynamics to plasma physics. In consequence, we analytically examine a two-dimensional generalized Bogoyavlensky-Konopelchenko equation in plasma physics in this paper. Firstly, the technique of Lie symmetry analysis of differential equations is used to find its symmetries and perform symmetry reductions to obtain ordinary differential equations which are solved to secure possible analytic solutions of the underlying equation. Then we use Kudryashov's and (G′/G)-expansion methods to acquire analytic solutions of the equation. As a result, solutions found in the process include exponential, elliptic, algebraic, hyperbolic and trigonometric functions which are highly important due to their various applications in mathematic and theoretical physics. Moreover, the obtained solutions are represented in diagrams. Conclusively, we construct conservation laws of the underlying equation through the use of multiplier approach. We state here that the results secured for the equation understudy are new and highly useful.

Eddy current damper (ECD), a contactless energy-dissipating device, is applying to control the vibration induced by earthquake and strong wind in civil structures. Combining with motion magnification mechanisms improves the damping effect of the ECD while significantly strengthens its nonlinearity. The response of single degree of freedom and multi-degree of freedom system with ECDs under a stationary stochastic earthquake characterized by the power spectral density function is evaluated using the stochastic linearization technique and expressions of the equivalent linear damping coefficient based on force criterion and energy criterion have been found, respectively. Comparisons with results obtained by Monte Carlo simulations confirm that for the nonlinearity of eddy current dampers the force-based criterion stochastic linearization technique gives accurate estimation.

We study the derivative nonlinear Schrödinger equation which has several applications, such as the propagation of circular polarized nonlinear Alfvén waves in plasmas. We present general and special solutions of this equation using first integrals. Classical Lie group theory along with power series method is also applied to obtain exact analytical solutions of this equation. Finally, conservation laws of the underlying equation are constructed through the use of the multiplier method.

This paper studies the third-order nonlinear deformed equation with variable coefficients, which is a generalization of CH, DP and DGH equations. Firstly, we investigate its conservation laws for different values of the three variable coefficients in the equation. Thereafter, we find principal Lie algebra of the equation and then find the coefficients that extends the principal Lie algebra. Finally, we present one symmetry reduction case.

The nonlinear phenomena in numbers are modelled in a wide range of fields such as chemical physics, ocean physics, optical fibres, plasma physics, fluid dynamics, solid-state physics, biological physics and marine engineering. This research article systematically investigates a (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation. We achieve a five-dimensional Lie algebra of the equation through Lie group analysis. This, in turn, affords us the opportunity to compute an optimal system of fourteen-dimensional Lie subalgebras related to the underlying equation. As a consequence, the various subalgebras are engaged in performing symmetry reductions of the equation leading to many solvable nonlinear ordinary differential equations. Thus, we secure different types of solitary wave solutions including periodic (Weierstrass and elliptic integral), topological kink and anti-kink, complex, trigonometry and hyperbolic functions. Moreover, we utilize the bifurcation theory of dynamical systems to obtain diverse nontrivial travelling wave solutions consisting of both bounded as well as unbounded solution-types to the equation under consideration. Consequently, we generate solutions that are algebraic, periodic, constant and trigonometric in nature. The various results gained in the study are further analyzed through numerical simulation. Finally, we achieve conservation laws of the equation under study by engaging the standard multiplier method with the inclusion of the homotopy integral formula related to the obtained multipliers. In addition, more conserved currents of the equation are secured through Noether’s theorem.

Background: The adoption of robotic platforms in upper gastrointestinal (GI) surgery is expanding rapidly. The absence of centralised guidance and governance in adoption of new surgical technologies may lead to an increased risk of patient harm., Methods: Surgeon stakeholders participated in a Delphi consensus process following a national open-invitation in-person meeting on the adoption of robotic upper GI surgery. Consensus agreement was deemed met if >80% agreement was achieved., Results: Following two rounds of Delphi voting, 25 statements were agreed on covering the training process, governance and good practice for surgeons' adoption in upper GI surgery. One statement failed to achieve consensus., Conclusions: These recommendations are intended to support surgeons, patients and health systems in the adoption of robotics in upper GI surgery.

Background: Radical surgery for esophageal cancer requires macroscopic and microscopic clearance of all malignant tissue. A critical element of the procedure is achieving a negative circumferential margin (CRM) to minimize local recurrence. The utility of minimally invasive surgery poses challenges in replicating techniques developed in open surgery, particularly for hiatal dissection in esophago-gastrectomy. In this study, the technical approach and clinical and oncological outcomes for open and laparoscopic esophago-gastrectomy are described with particular reference to CRM involvement., Materials and Methods: This cohort study included all patients undergoing either open or laparoscopic esophago-gastrectomy between January 2004 and June 2022 in a single tertiary center. A standard surgical technique for hiatal dissection of the esophago-gastric junction developed in open surgery was adapted for a laparoscopic approach. Clinical parameters, length of stay (LOS), postoperative complications, and mortality data were collected and analyzed by a Mann-Whitney U or Fisher's exact method., Results: Overall 447 patients underwent an esophago-gastrectomy in the study with 219 open and 228 laparoscopic procedures. The CRM involvement was 18.8% in open surgery and 13.6% in laparoscopic surgery. The 90-day-mortality for open surgery was 4.1 compared with 2.2% for laparoscopic procedures. Median Intensive care unit (ITU), inpatient LOS and 30-day readmission rates were shorter for laparoscopic compared with open esophago-gastrectomy (ITU: 5 versus 8 days, P= 0.0004; LOS: 14 versus 20 days, P= 0.022; 30-day re-admission 7.46 versus 10.50%). Postoperative complication rates were comparable across both cohorts. The rates of starting adjuvant chemotherapy were 51.8 after open and 74.4% in laparoscopic esophago-gastrectomy., Conclusion: This study presents a standardized surgical approach to hiatal dissection for esophageal cancer. The authors present equivalence between open and laparoscopic esophago-gastrectomy in clinical, oncological, and survival outcomes with similar rates of CRM involvement. The authors also observe a significantly shorter hospital length of stay with the minimally invasive approach., (Copyright © 2024 The Author(s). Published by Wolters Kluwer Health, Inc.)

Introduction: The OligoMetastatic Esophagogastric Cancer (OMEC) project aims to provide clinical practice guidelines for the definition, diagnosis, and treatment of esophagogastric oligometastatic disease (OMD)., Methods: Guidelines were developed according to AGREE II and GRADE principles. Guidelines were based on a systematic review (OMEC-1), clinical case discussions (OMEC-2), and a Delphi consensus study (OMEC-3) by 49 European expert centers for esophagogastric cancer. OMEC identified patients for whom the term OMD is considered or could be considered. Disease-free interval (DFI) was defined as the time between primary tumor treatment and detection of OMD., Results: Moderate to high quality of evidence was found (i.e. 1 randomized and 4 non-randomized phase II trials) resulting in moderate recommendations. OMD is considered in esophagogastric cancer patients with 1 organ with ≤ 3 metastases or 1 involved extra-regional lymph node station. In addition, OMD continues to be considered in patients with OMD without progression in number of metastases after systemic therapy. 18 F-FDG PET/CT imaging is recommended for baseline staging and for restaging after systemic therapy when local treatment is considered. For patients with synchronous OMD or metachronous OMD and a DFI ≤ 2 years, recommended treatment consists of systemic therapy followed by restaging to assess suitability for local treatment. For patients with metachronous OMD and DFI > 2 years, upfront local treatment is additionally recommended., Discussion: These multidisciplinary European clinical practice guidelines for the uniform definition, diagnosis and treatment of esophagogastric OMD can be used to standardize inclusion criteria in future clinical trials and to reduce variation in treatment., Competing Interests: Declaration of Competing Interest Dr. van Laarhoven reports a consultant or advisory role: Amphera, Anocca, Astellas, AstraZeneca, Beigene, Boehringer, Daiichy-Sankyo, Dragonfly, MSD, Myeloid, Servier; Research funding, medication supply, and/or other research support: Auristone, Incyte, Merck, ORCA, Servier; Speaker role: Astellas, Beigene, Benecke, BMS, Daiichy-Sankyo, JAAP, Medtalks, Novartis, Springer, Travel Congress Management B.V. Dr. Muijs reports institutional grants from: Elekta, IBA, RaySearch, Siemens, Mirada, Bergoz Instrumentation and Medical Data Works, KWF, all outside the submitted work. Dr. van Hillegersberg has a consulting and advisory role at Intuitive Surgical, Medtronic, Olympus and J&J Ethicon. Dr. de Manzoni reports personal fees from Lilly, outside the submitted work. Dr. Gani reports travel grants from Elekta and departmental research cooperation, outside the submitted work. Dr. Smyth is supported by the NIHR Biomedical Research Centre at Oxford (the views expressed in this Article are those of the authors and not necessarily those of the National Health Service, the NIHR, or the Department of Health) and resports personal fees/grants from: Astra Zeneca, Beigene, BMS, Amal Therapeutics, Amgen, Daiichi Sankyo, Merck, Servier, Novartis, Pfizer, Roche, and Zymeworks, all outside the submitted work. Dr. Haj Mohammad reports consulation fees from: Merck, BMS, Eli Lilly, Astra Zeneca, and research funding from Servier, all outside the submitted work. Dr. Adenis reports grants and personal fees from Bayer, personal fees and non-financial support from MSD, personal fees from: BMS, Novartis, Pierre-Fabre, non-financial support from Servier, grants from Sanofi, all outside the submitted work. Dr. Lordick reports grants from: BMS and Gilead, personal fees from: Amgen, Astellas, Bayer, BMS, Daiichi Sankyo, Eli Lilly, Elsevier, Incyte, Merck, MSD, Roche, Servier, all outside the submitted work. Dr. Slingerland reports an advisory role at BMS and Lilly. Dr. van Berge Henegouwen received researcher-initiated grant from Stryker and is consultant for Alesi Surgical, Johnson and Johnson, Medtronic, BBraun and Viatris. Dr Nilsson reports advisory roles for BMS and Medtronic. Dr. Tabernero reports personal financial interest in form of scientific consultancy role for Array Biopharma, AstraZeneca, Avvinity, Bayer, Boehringer Ingelheim, Chugai, Daiichi Sankyo, F. Hoffmann-La Roche Ltd, Genentech Inc, HalioDX SAS, Hutchison MediPharma International, Ikena Oncology, IQVIA, Lilly, Menarini, Merck Serono, Merus, MSD, Mirati, Neophore, Novartis, Orion Biotechnology, Peptomyc, Pfizer, Pierre Fabre, Samsung Bioepis, Sanofi, Seattle Genetics, Servier, Taiho, Tessa Therapeutics and TheraMyc; and also educational collaboration with Imedex, Medscape Education, MJH Life Sciences, PeerView Institute for Medical Education and Physicians Education Resource (PER). Dr. Tabernero declares institutional financial interest in form of financial support for clinical trials or contracted research for Amgen Inc, Array Biopharma Inc, AstraZeneca Pharmaceuticals LP, BeiGene, Boehringer Ingelheim, Bristol Myers Squibb, Celgene, Debiopharm International SA, F. Hoffmann-La Roche Ltd, Genentech Inc, HalioDX SAS, Hutchison MediPharma International, Janssen-Cilag SA, MedImmune, Menarini, Merck Health KGAA, Merck Sharp & Dohme, Merus NV, Mirati, Novartis Farmacéutica SA, Pfizer, Pharma Mar, Sanofi Aventis Recherche & Développement, Servier, Taiho Pharma USA Inc, Spanish Association Against Cancer Scientific Foundation and Cancer Research UK. Dr. Nieuwenhuijzen reports advisory/speaker roles from Medtronic and Lilly. All remaining authors have declared no conflict of interest., (Copyright © 2024 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Background: Currently, little is known regarding the optimal technique for the abdominal phase of RAMIE. The aim of this study was to investigate the outcome of robot-assisted minimally invasive esophagectomy (RAMIE) in both the abdominal and thoracic phase (full RAMIE) compared to laparoscopy during the abdominal phase (hybrid laparoscopic RAMIE)., Methods: This retrospective propensity-score matched analysis of the International Upper Gastrointestinal International Robotic Association (UGIRA) database included 807 RAMIE procedures with intrathoracic anastomosis between 2017 and 2021 from 23 centers., Results: After propensity-score matching, 296 hybrid laparoscopic RAMIE patients were compared to 296 full RAMIE patients. Both groups were equal regarding intraoperative blood loss (median 200 ml versus 197 ml, p = 0.6967), operational time (mean 430.3 min versus 417.7 min, p = 0.1032), conversion rate during abdominal phase (2.4% versus 1.7%, p = 0.560), radical resection (R0) rate (95.6% versus 96.3%, p = 0.8526) and total lymph node yield (mean 30.4 versus 29.5, p = 0.3834). The hybrid laparoscopic RAMIE group showed higher rates of anastomotic leakage (28.0% versus 16.6%, p = 0.001) and Clavien Dindo grade 3a or higher (45.3% versus 26.0%, p < 0.001). The length of stay on intensive care unit (median 3 days versus 2 days, p = 0.0005) and in-hospital (median 15 days versus 12 days, p < 0.0001) were longer for the hybrid laparoscopic RAMIE group., Conclusions: Hybrid laparoscopic RAMIE and full RAMIE were oncologically equivalent with a potential decrease of postoperative complications and shorter (intensive care) stay after full RAMIE., (© 2023. The Author(s).)

Background: Local treatment improves the outcomes for oligometastatic disease (OMD, i.e. an intermediate state between locoregional and widespread disseminated disease). However, consensus about the definition, diagnosis and treatment of oligometastatic oesophagogastric cancer is lacking. The aim of this study was to develop a multidisciplinary European consensus statement on the definition, diagnosis and treatment of oligometastatic oesophagogastric cancer., Methods: In total, 65 specialists in the multidisciplinary treatment for oesophagogastric cancer from 49 expert centres across 16 European countries were requested to participate in this Delphi study. The consensus finding process consisted of a starting meeting, 2 online Delphi questionnaire rounds and an online consensus meeting. Input for Delphi questionnaires consisted of (1) a systematic review on definitions of oligometastatic oesophagogastric cancer and (2) a discussion of real-life clinical cases by multidisciplinary teams. Experts were asked to score each statement on a 5-point Likert scale. The agreement was scored to be either absent/poor (<50%), fair (50%-75%) or consensus (≥75%)., Results: A total of 48 experts participated in the starting meeting, both Delphi rounds, and the consensus meeting (overall response rate: 71%). OMD was considered in patients with metastatic oesophagogastric cancer limited to 1 organ with ≤3 metastases or 1 extra-regional lymph node station (consensus). In addition, OMD was considered in patients without progression at restaging after systemic therapy (consensus). For patients with synchronous or metachronous OMD with a disease-free interval ≤2 years, systemic therapy followed by restaging to consider local treatment was considered as treatment (consensus). For metachronous OMD with a disease-free interval >2 years, either upfront local treatment or systemic treatment followed by restaging was considered as treatment (fair agreement)., Conclusion: The OMEC project has resulted in a multidisciplinary European consensus statement for the definition, diagnosis and treatment of oligometastatic oesophagogastric adenocarcinoma and squamous cell cancer. This can be used to standardise inclusion criteria for future clinical trials., Competing Interests: Conflict of interest statement The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Dr. van Laarhoven reports grants or advisory/speaker role from: Astellas, BMS, Dragonfly, Lilly, Merck, Novartis, Nordic Pharma, Servier; research funding or medical supply from: Bayer, BMS, Celgene, Janssen, Incyte, Lilly, Merck, Nordic Pharma, Philips, Roche, Servier; and has received unrestricted research funding (non-commercial) from: Dutch Cancer Society, NWO/ZonMw, European Research Council, MaagLeverDarm Stichting. Dr. Muijs reports institutional grants from: Elekta, IBA, RaySearch, Siemens, Mirada, Bergoz Instrumentation and Medical Data Works, KWF, all outside the submitted work. Dr. van Hillegersberg has a consulting and advisory role at Intuitive Surgical. Dr. de Manzoni reports personal fees from Lilly, outside the submitted work. Dr. Gani reports travel grants from Elekta and departmental research cooperation, outside the submitted work. Dr. Smyth reports personal fees/grants from: Astra Zeneca, Beigene, BMS, Amal Therapeutics, Amgen, Daiichi Sankyo, Merck, Servier, Novartis, Pfizer, Roche, and Zymeworks, all outside the submitted work. Dr. Haj Mohammad reports consulation fees from: Merck, BMS, Eli Lilly, Astra Zeneca, and research funding from Servier, all outside the submitted work. Dr. Adenis reports grants and personal fees from Bayer, personal fees and non-fianciel support from MSD, personal fees from: BMS, Novartis, Pierre-Fabre, non-financial support from Servier, grants from Sanofi, all outside the submitted work. Dr. Lordick reports grants from: BMS and Gilead, personal fees from: Amgen, Astellas, Bayer, BMS, Daiichi Sankyo, Eli Lilly, Elsevier, Incyte, Merck, MSD, Roche, Servier, all outside the submitted work. Dr. Slingerland reports an advisory role at BMS and Lilly. Dr. van Berge Henegouwen received researcher-initiated grant from Stryker and is consultant for Alesi Surgical, Johnson and Johnson, Medtronic, Braun and Mylan. Dr Nilsson reports advisory roles for BMS and Medtronic. All remaining authors have declared no conflict of interest., (Copyright © 2023 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Background: A uniform definition and treatment for oligometastatic esophagogastric cancer is currently lacking. However, a comprehensive definition of oligometastatic esophagogastric cancer is necessary to initiate studies on local treatment strategies (e.g. metastasectomy or stereotactic radiotherapy) and new systemic therapy agents in this group of patients. For this purpose, the OligoMetastatic Esophagogastric Cancer (OMEC) project was established. The OMEC-project aims to develop a multidisciplinary European consensus statement on the definition, diagnosis, and treatment for oligometastatic esophagogastric cancer and provide a framework for prospective studies to improve outcomes of these patients., Methods: The OMEC-project consists of five studies, including 1) a systematic review on definitions and outcomes of oligometastatic esophagogastric cancer; 2) real-life clinical scenario discussions in multidisciplinary expert teams to determine the variation in the definition and treatment strategies; 3) Delphi consensus process through a starting meeting, two Delphi questionnaire rounds, and a consensus meeting; 4) publication of a multidisciplinary European consensus statement; and 5) a prospective clinical trial in patients with oligometastatic esophagogastric cancer., Discussion: The OMEC project aims to establish a multidisciplinary European consensus statement for oligometastatic esophagogastric cancer and aims to initiate a prospective clinical trial to improve outcomes for these patients. Recommendations from OMEC can be used to update the relevant guidelines on treatment for patients with (oligometastatic) esophagogastric cancer., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Dr. Hawkins reports grants from NIHRBiomedical Research Centre at University College London Hospitals NHS Foundation Trust, outside the submitted work; Dr. Smyth reports personal fees from AMAL Therapeutics, Astellas Pharma, AstraZeneca, Beigene, Five Prime Therapeutics, Merck, Pfizer, Roche, Servier and Zymeworks and institutional funding for clinical trials research from Astra Zeneca, Astellas, Basilea, BMS, Daiichi Sankyo, Roche, Macrogenics and MSD. Dr. Moehler reports grants and non-financial support from EORTC, grants and non-financial support from AIO, grants and non-financial support from German Cancer Aid, grants and non-financial support from BMBF, during the conduct of the study; personal fees from Falk Foundation, personal fees from Lilly, grants and personal fees from MSD, personal fees from Roche, grants and personal fees from Pfizer, grants, personal fees and non-financial support from Amgen, grants, personal fees and non-financial support from Bristol-Myers Squibb, grants and personal fees from Merck Serono, personal fees from MCI Group, personal fees from Taiho, outside the submitted work; Dr. van Laarhoven reports consultant or advisory role: BMS, Dragonfly, Lilly, Merck, Nordic Pharma, Servier, outside the submitted work; research funding and/or medication supply: Bayer, BMS, Celgene, Janssen, Incyte, Lilly, Merck, Nordic Pharma, Philips, Roche, Servier, outside the submitted work; Dr. van Hillegersberg is proctor for Intuitive Surgical and consultant for Medtronic, the other authors have nothing to disclose., (Copyright © 2022 The Authors. Published by Elsevier Ltd.. All rights reserved.)