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Nonlinear partial differential equations (NLPDEs) have emerged as a major focus of study in a variety of nonlinear science disciplines. This is because in general, mathematical, physics and engineering problems may be stated by NLPDEs. It may be noted that a specific kind of exact/analytical solution called traveling wave solutions for NLPDEs has great significance. In this regard, this paper addresses the traveling wave solution to the new coupled Konno–Oono equation (NCKOE), a set of NLPDE. A traveling wave transformation and the Riccati–Bernoulli sub-ode method (RBSOM) are used here to retrieve the exact/analytical traveling wave solution of the NCKOE. By using the above-mentioned approach, NLPDEs can be updated toward a collection of algebraic equations. Further, different types of solitary wave solitons, Trigonometric function solutions, Hyperbolic soliton solutions and dark bright solitons to the NCKOE have been successfully retrieved. Importantly, the newly derived solutions adhere to the main equation when they are inserted into the governing equations. Furthermore, through an appropriate selection of parameters, three-dimensional and two-dimensional figures are presented for physical illustration of the obtained solutions. These visual representations serve to showcase the effectiveness, conciseness and efficiency of the applied techniques. [ABSTRACT FROM AUTHOR]

This article investigates the traveling wave solution for a geophysical Boussinesq-type equation that models equatorial tsunami waves. The discussed structure exhibits explicit traveling wave solutions characterized by speeds surpassing the linear propagation speed and small amplitude wave near-field variables. A combination of traveling wave transformation, tanh method, extended tanh method, and a modified form of extended tanh method are implemented, leading to some new traveling wave solutions for the referred nonlinear model. Through the appropriate selection of parameters, the research employs two-dimensional, three-dimensional, and contour plots to showcase the characteristics of specific solutions. The presented visual representation serves as an efficient means to understand the nature of these solutions. This research further extends its investigation by transforming the considered equation into a planar dynamical structure. Through this transformation, all potential phase portraits of the dynamical system are thoroughly examined, utilizing the theory of bifurcation. In addition, this work investigates the modulation of instability in the governing equation using the linear stability analysis function. Importantly, all the newly derived solutions conform to the main equation when substituted into it. The obtained results demonstrate the effectiveness, conciseness, and efficiency of the applied techniques. These strategies have the potential to be useful in scrutinizing more complex models that appear in modern science and engineering. [ABSTRACT FROM AUTHOR]

The interest and importance of studying the reproductive strategies of Palaeozoic plants are growing. Fossil seeds play an essential role in this line of study, as they are widely described from different sedimentary formations throughout the Permian period. The Indian Permian Seed Database (IPSD) software will be an information system for ensuring the storage, safety, accessibility and recovery of the details of Indian Permian seed records in a selective manner. The current database includes 28 genera and 44 species of compressed seeds described from Lower Gondwana (Permian), with all the details for researchers. The software provides options for addition, deletion, modification and search facility. The search also includes different options (single or combination). It is a quick and organised way to look for seeds, especially on a data grid for information about seeds that have already been published in the same or different sediments. IPSD is a tool for the computer-based identification of seeds and distinguishing different genera or species within the same category. It is user-friendly and provides updated knowledge of seeds from the Lower Gondwana basins of India. It provides morphotaxonomical characters, distribution and photo documentation of seeds. The software increases accuracy through computerassisted identification of seeds. Hence, reducing and curtailing unnecessary information while describing a new species with inadequate earlier knowledge of Permian seeds. [ABSTRACT FROM AUTHOR]

In this manuscript, a new hybrid technique viz Sawi transform-based homotopy perturbation method is implemented to solve one-dimensional shallow water wave equations. In general, the quantities involved with such equations are commonly assumed to be crisp, but the parameters involved in the actual scenario may be imprecise/uncertain. Therefore, fuzzy uncertainty is introduced as an initial condition. The main focus of this study is to find the approximate solution of one-dimensional shallow water wave equations with crisp, as well as fuzzy, uncertain initial conditions. First, by taking the initial condition as crisp, the approximate series solutions are obtained. Then these solutions are compared graphically with existing solutions, showing the reliability of the present method. Further, by considering uncertain initial conditions in terms of Gaussian fuzzy number, the governing equation leads to fuzzy shallow water wave equations. Finally, the solutions obtained by the proposed method are presented in the form of Gaussian fuzzy number plots. [ABSTRACT FROM AUTHOR]

A palaeofloristic study and geochemical analysis of a Permian section in Ib River Basin near Ustali village, Odisha State has been undertaken. The complete macrofloral assemblage comprising 44 taxa belong to the orders Equisetales, Sphenophyllales, Filicales, and Glossopteridales. A marked floral change has been noticed in two fossiliferous horizons of this section, demonstrating the existence of two different floral zones in Raniganj Formation rocks of this section. The upper floral zone is assigned to the Wuchiapingian, while the lower floral zone is of Wordian‐Capitanian age. The occurrence of Gangamopteris is the first report of this genus from the Raniganj Formation of the Ib River Basin, as well as from the Son‐Mahanadi Master Basin. The existence of tiny seeds infers the prevalence of arid and warm climatic conditions at least during the blossoming and seed development phase, resulting in a sluggish inflow of nutrients to the growing seeds, thereby restricting their proper growth. The palynoassemblage confirms its resemblance with the Raniganj palynoflora of Wordian‐Capitanian affinity. Biomarker analysis indicates a good contribution of algal and microbial organic matter during the deposition, however, the overall biomarker composition and distribution suggests an increased thermal maturity of the studied samples. [ABSTRACT FROM AUTHOR]