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This paper brings together methods to solve and/or characterize solutions of some problems of mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. Using surjectivity or variational approaches, one may obtain or characterize weak solutions for Dirichlet or Newmann problems for these important operators. This article details three ways to use surjectivity results for a special type of operator involving the duality mapping and a Nemytskii operator, three methods starting from Ekeland's variational principle and, lastly, one with a generalized variational principle to solve or describe the above-mentioned solutions. The relevance of these operators and the possibility of their involvement in the modeling of an important class of real phenomena determined the author to group these seven procedures together, presented in detail, followed by many applications, accompanied by a general overview of specialty domains. The use of certain variational methods facilitates the complete solution of the problem via appropriate numerical methods and computational algorithms. The exposure of the sequence of theoretical results, together with their demonstration in as much detail as possible has been fulfilled as an opportunity for the complete development of these topics. [ABSTRACT FROM AUTHOR]

Attitude is one aspect that needs to be considered both for learning activities or learning objects. This study aims to determine the attitudes and motivations of students in mathematics physics subjects. The sample used was 100 students who had studied the Mathematics Physics course. This study employed quantitative research methods with correlational research design. Respondent was gathered by purposive sampling method. The research instruments used were attitude questionnaires in mathematical physics and motivational questionnaires. The study found that there is a significant relationship between attitudes and motivation of students in mathematics physics learning.

In addition, this Special Issue addressed other qualitative properties of linear and nonlinear equations and systems of mathematical physics, such as scattering theory, inverse problems, variational methods, and variational calculus. One paper, [[11]], deals with the problem of determining the Hill equation (or the one-dimensional Schrödinger equation) based on its spectrum and deriving the Hill equation from the specific properties of its discriminant. The main approach to studying the problem under consideration was based on the spectral theory of differential operators as well as on the properties of the spectrum HT ht of the one-dimensional Schrödinger operator HT ht with periodic coefficients HT ht and HT ht . B Differential Equations of Mathematical Physics b : In the section on Differential Equations of Mathematical Physics, questions related to the solvability, regularity, stability, and asymptotic behavior of solutions to the equations of mathematical physics and PDE, including the hydrodynamic (Stokes equations) and Helmgotz equations, were proposed for consideration. [Extracted from the article]

AbstractNonlinear partial differential equations (NLPDEs) are widely utilized in engineering and physical research to represent many physical processes of naturalistic occurrences. In this paper, we investigate two well-known NLPDEs, namely, the (2 + 1)-dimensional first integro-differential KP hierarchy equation and the (2 + 1)-dimensional second integro-differential KP hierarchy equation, through a well-stable algorithm known as the [Formula: see text]-expansion approach for the first time. This algorithm is generally based on the expansion of function method and has the advantage of easy implementation and can provide a reliable solution to any NLPDEs. Employing the algorithm, we have been able to perceive the closed form solitons of the two chosen NLPDEs that physically represent the solitary wave solutions like, singular, singular periodic, bell, and anti-bell-shaped types of solitons. Furthermore, we explore the graphical manifestations of the obtained solutions, which are of the mentioned soliton types. From the findings of our in-depth study, we can state that the acquired solutions for the selected two equations may greatly aid to extracting the associated natural phenomena in mathematical physics such as fluid dynamics and ocean engineering.

In this study, we utilize the potent generalized Kudryashov method to address the intricate obstacles presented by fractional differential equations in the field of mathematical physics. Specifically, our focus centers on obtaining novel exact solutions for three pivotal equations: the time-fractional seventh-order Sawada-Kotera-Ito equation, the time-fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation, and the time-fractional seventh-order Kaup–Kupershmidt equation. The generalized Kudryashov method, celebrated for its versatility and efficacy in addressing intricate nonlinear problems, plays a central role in our research. This method not only simplifies the equations but also unveils their inner dynamics, rendering them amenable to meticulous analysis. It is worth noting that our fractional derivatives are defined in the context of the conformable fractional derivative, providing a solid foundation for our mathematical investigations. One notable aspect of our study is the visual representation of our findings. Graphical representations of the yielded solutions enliven intricate mathematical structures, providing a concrete insight into the dynamics and behaviors of said equations. This paper highlights the proficiency of the generalized Kudryashov method in resolving complex issues presented by fractional differential equations. Our study not only broadens the range of mathematical methods but also enhances our comprehension of the intriguing realm of nonlinear physical phenomena. [ABSTRACT FROM AUTHOR]

Abstract This article effectively establishes the exact soliton solutions for the Boussinesq model, characterized by time-dependent coefficients, employing the advanced modified simple equation, generalized Kudryashov and modified sine–Gordon expansion methods. The adaptive applicability of the Boussinesq system to coastal dynamics, fluid behavior, and wave propagation enriches interdisciplinary research across hydrodynamics and oceanography. The solutions of the system obtained through these significant techniques make a path to understanding nonlinear phenomena in various fields, surpassing traditional barriers and further motivating research and application. Significant impacts of the coefficients of the equation, wave velocity, and related parameters are evident in the profiles of soliton-shaped waves in both 3D and 2D configurations when all these factors are treated as variables, which are not seen in the case for constant coefficients. This study enhances the understanding of the significant role played by nonlinear evolution equations with time-dependent coefficients through careful dynamic explanations and detailed analyses. This revelation opens up an interesting and challenging field of study, with promising insights that resonate across diverse scientific disciplines.

AbstractThe (3 + 1)-dimensional Kadomtsev–Petviashvili equation has significant applications that emerge in the study of fluids and multi-component plasmas. The main object of our study is to investigate stable and efficient solitary solutions to the stated wave equations through two different schemes that provide generic solutions like exponential functions, trigonometric functions, hyperbolic functions, etc. The graphical illustrations for different values of the corresponding parameters of the attained solutions are explained in order to expose the intimate structure of the substantial phenomena. In particular, changes in wave position and category with respect to time are deliberated extensively through 2D figures. It has been found that wave velocity depends on some free parameters associated with the methods used to solve the equation. It has been demonstrated that for different values of the free parameters, the obtained solutions of the KP model exhibit dark soliton, peakon shape soliton, dark soliton-type wave, bright soliton, bell-shaped soliton, etc. Moreover, the direction and position of the solitons for the variation of other parameters are measured, from which a simple and comprehensive interpretation of the various aspects of water waves can be obtained. We think the obtained solution could be highly useful for studying nonlinear events in fluid dynamics, wind waves, and wind-generated waves.

Mathematical Physics I is one of the courses that train students to think critically and creatively in the learning process. Therefore in this research developed a teaching material in the form of modules based on Problem Based Instruction (PBI). The module began with introduce students to a contextual problem that later ended with the presentation and analysis of student work. This type of research is the development of research using a stage model of Plomp, namely: (1) preliminary research, (2) prototyping phase, and (3) assessment phase.The research subjects involved lecturers and students from two campuses, namely Universitas Negeri Padang and STKIP PGRI West Sumatra. The research data was obtained through the validation sheet of modules that look at the feasibility module by module construction, content and the language used. Item analysis was conducted by using qualitative and quantitative analysis.Based on the results of the validation, results showed that the modules are very valid and ready for trial eligibility to students. Modules that are designed are categorized as very valid with a value of 84.66 and very practical with a practical value of 83.05.This result indicate that developmentof Mathematical Physics I module based on the Problem Based Instruction learning model can be used by students and lectures in learning process.

In this paper, we consider two nonlinear models arising in mathematical physics, namely, the Landau–Ginzburg–Higgs (LGH) equation and the nonlinear dispersive modified Benjamin–Bona (DMBBM) equation. The LGH model describes the exchange between mid-latitude Rossby and equatorial waves, as well as nonlinear waves with long-range and weak scattering interactions between tropical tropospheres and mid-latitude. The DMBBM model explains surface wave propagation estimates in a nonlinear dispersive medium. We employed He’s semi-inverse approach in order to solve these models. Specifically, we present hyperbolic wave solutions. The proposed method is straightforward, reliable, and effective, and its potential for use in solving additional partial differential equations in applied research is encouraging. Appropriate values for the parameters are taken into consideration when simulating certain 2D and 3D graphs that correspond to select solutions using Matlab software.

In this manuscript, the primary motivation is the implementation of the advanced exp − ϕ ξ -expansion method to construct the soliton solution, which contains some controlling parameters of two distinct equations via the Biswas–Arshed model and the (3 + 1)-dimensional Kadomtsev–Petviashvili equation. Here, the solutions' behaviors are presented graphically under some conditions on those parameters. The height of the wave, wave direction, and angle of the obtained wave is formed by substituting the particular values of the considerations over showing figures with the control plot. With the collaboration of the advanced exp − ϕ ξ -expansion method, we construct entirely the solitary wave results as well as rogue type soliton, combined singular soliton, kink, singular kink, bright and dark soliton, periodic shape, double periodic shape soliton, etc. Therefore, it is remarkable to perceive that the advanced exp − ϕ ξ -expansion technique is a simple, viable, and numerical solid apparatus for clarifying careful outcomes to the other nonstraight equivalences. [ABSTRACT FROM AUTHOR]

Numerous complex situations arising from science and engineering are modeled by integral-differential equations (IDEs). Examples of these situations include mathematical modeling of infectious diseases, epidemics, circuit analysis, voltage drop equations, computational neuroscience, intergalactic modeling, and many more. To explain the mathematical structure and the behavior of various phenomena in nature, two equations with simple mathematical structure namely: the (1 + 1)-dimensional integro-differential Ito equation (IDIE) and the (2 + 1)-dimensional integro-differential Sawada-Kotera equation (IDSKE) are considered. In this analytical investigation, we have conducted an in-depth enquiry to trace the distinctive closed form progressive wave solutions of these proposed models using the (G′G′+G+A)-expansion method. The graphical forms of the acquired solutions have been displayed in the bell-shaped soliton, singular periodic, and anti-kink shape soliton solutions after the values for the free parameters were specified. The two non-algebraic solutions, named, exponential and trigonometric function solutions, have emerged by applying our proposed method. Based on the general findings of our investigation for different parametric values, the attained wave solutions revealed can keep a vital role for natural balances and can be engaged in modern physical applications. The parameters have a visible effect on the wave amplitude and the swiftness of the traveling wave. The executed outcomes are innovative and have monumental applications in the present research, especially in the fields of theoretical physics, astrophysics, plasma physics, particle physics, theory of relativity, advance quantum mechanics, string theory, and geotechnical engineering.

This paper brings together methods to solve and/or characterize solutions of some problems of mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. Using the widely debated results of surjectivity or variational approaches, one may obtain or characterize weak solutions for Dirichlet or Newmann problems for these important operators. The relevance of these operators and the possibility to be involved in the modeling of an important class of real phenomena is once again revealed by their applications. The use of certain variational methods facilitates the complete solution of the problem using appropriate numerical methods and computational algorithms. Some theoretical results are involved to complete the solutions for a sequence of models issued from real phenomena drawing. [ABSTRACT FROM AUTHOR]

In this article, we investigated the Landau–Ginzburg–Higgs (LGH) equation, focusing on the analysis of isolated soliton solutions and their stability. To compute the isolated soliton solutions, we used the advanced auxiliary equation (AAE) approach, which has proven to be a powerful and efficient method for extracting soliton solutions in various nonlinear partial differential equations (NLPDEs). We provided a detailed explanation, both graphically and physically, of the obtained soliton solutions in this article. Furthermore, we used the linear stability technique to conduct a stability analysis of the LGH equation. Additionally, we studied the bifurcation and stability of the equilibria and performed phase plane analysis of the model. We also provided a discussion on the comparisons between the AAE method and two other well-known approaches: the generalized Kudryashov method and the improved Bernoulli sub-equation function method. The application of the AAE approach in this study demonstrates its effectiveness and capability in analysing and extracting soliton solutions in NLPDEs.

The reviewers contacted by the editors to evaluate this work have been unable to confirm that the main results are correct. Flaws that were identified by the reviewers in earlier versions of the paper have been addressed by the author. Although it is possible that future research will uncover a significant mistake in this paper or show that the conclusions are in error, I believe that publishing it may benefit the readership of the Journal and stimulate further work in mathematical physics on an important topic.

The aim of this study is comparing math anxiety of secondary school female students in groups (Science and Mathematical Physics) Public Schools, district 2, city of Sari. The purpose of the research is applied research, it is a development branch, and in terms of the nature and method, it is a causal-comparative research. The statistical population in this study consisted of all secondary school female students in groups (Science and Mathematical Physics) Public Schools, district 2, city of Sari that is the equivalent of 1,900 people according to the latest figures cast of Education in Sari city. According to the population size and referring to the Morgan's sample size table, the sample size was considered 320 people. Simple random sampling method was used to select research samples. Data collection methods included library and observation. Data collection tool in the survey is questionnaire. Pelick and Parker (1982) math anxiety questionnaire that their reliability was calculated 0.98 by using Cronbach's alpha. Research Hypothesis test and data derived from questionnaires were analyzed by using SPSS software and descriptive and inferential statistics. The tests used in the research included Kolmogorov-Smirnov test and Pearson correlation and T of two independent groups. The results show a difference between math anxiety among students of mathematics and science. According to the average score of students' math anxiety, we find out students' math anxiety in science is more than math. There is an inverse relationship between math anxiety and students' academic achievement. Students, who have high math anxiety, have lower academic achievement.

The (2 + 1)-dimensional Konopelchenko-Dubrovsky (KD) model and the modified version of the new Kudryashov (MVNK) technique are chosen in the current research to obtain the traveling wave solutions (TWSs). The obtained solutions represent the rich range of explicit solutions to the studied model. As a result, TWSs to the stated model are expressed as the different types of wave profiles such as the kink shape, bell shape, anti-bell shape, and W-shape wave profiles. The Hamiltonian function is found from the stated model and shown it as three dimensional, contour and phase plane in this manuscript. The effects of wave velocity and other parameters on the wave profile are also discussed. The obtained wave profiles are typically useful in applications how waves interact with high-dimensional systems in new, specialized structures. Additionally, the direction and position of solitons for changing other parameters can offer a clear-cut explanation of all the different features of wind and water waves. It is seen that the mentioned scheme is effective, potential and easy in mathematical physics. Finally, this study may be opened up brand-new avenues for further study and application in the fields of mathematical physics.

Problem and goal. Currently, information and telecommunications technologies are widely used in the professional activities of most specialists in various subject areas. This circumstance initiates the training of students in higher education institutions, who must have not only deep subject knowledge, but also be able to master modern information and telecommunications technologies and be able to apply them in their activities. One of the fundamental disciplines that is included in the university curricula for preparing students of physical and mathematical fields of study is Equations of mathematical physics. In the process of teaching students the equations of mathematical physics, the goals are set not only to form students' solid subject knowledge, but also to acquire the skills and abilities to apply modern information technologies in the study of mathematical models based on the equations of mathematical physics. Methodology. Educational electronic resources are used in training sessions on mathematical physics equations. Such training sessions with students take place in the form of laboratory classes, where modern computer technologies are used to find solutions to equations of mathematical physics and then analyze them. Results . The implementation of didactic principles of teaching mathematical physics equations in laboratory classes using educational electronic resources allows students to achieve good results in the methods of studying mathematical physics equations. Conclusion. The use of educational electronic resources in the classroom on the equations of mathematical physics allows students, in addition to deep subject knowledge, to acquire the skills and abilities to use modern computer techno- logies to solve mathematical problems.

In this paper, we study the analytic ranks of the Hasse–Weil L-function. We consider the products for the completed Hasse–Weil L-function in the framework of the theory of modular forms. We propose the new conjectures for the deformed Fourier sine and cosine integral formulas related to the completed Hasse–Weil L-functions and Mittag-Leffler function. We show the entire-function solutions for the fractional diffusion equations in mathematical physics. We also discuss the trivial zeros of the Hasse–Weil L-function. [ABSTRACT FROM AUTHOR]