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Painlevé integrability and a collection of new wave structures related to an important model in shallow water waves

Communications in Theoretical Physics 2023年第7期75卷 70-80页

作者： Isma Ghulam Murtaza Nauman Raza Saima Arshed Department of Mathematics University of the PunjabLahore 54590Pakistan

This paper investigates the perturbed Boussinesq equation that emerges in shallow water *** perturbed Boussinesq equation describes the properties of longitudinal waves in bars,long water waves,plasma waves,quantum mechanics,acoustic waves,nonlinear optics,and other *** a result,the governing model has significant importance in its own *** singular manifold method and the unified methods are employed in the proposed model for extracting hyperbolic,trigonometric,and rational function *** solutions may be useful in determining the underlying context of the physical *** is worth noting that the executed methods are skilled and effective for examining nonlinear evaluation equations,compatible with computer algebra,and provide a wide range of wave *** addition to this,the Painlevétest is also used to check the integrability of the governing ***-dimensional and threedimensional plots are made to illustrate the physical behavior of the newly obtained exact *** makes the study of exact solutions to other nonlinear evaluation equations using the singular manifold method and unified technique prospective and deserving of further study.

关键词： soliton shallow water waves singular manifold method Painleve test

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Darboux Transformation and Soliton Solutions for the (2+1)-Dimensional Generalization of Shallow Water Wave Equation with Symbolic Computation

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Communications in Theoretical Physics 2013年第8期60卷 194-200页

作者：闻小永孟祥花 Department of Mathematics School of Applied ScienceBeijing Information Science and Technology University

In this paper, the （2＋l）-dimensional generalization of shallow water wave equation, which may be used to describe the propagation of ocean waves, is analytically investigated. With the aid of symbolic computation, we prove that the （2＋ l）-dimensional generalization of shallow water wave equation possesses the Palnlev6 property under a certain condition, and its Lax pair is constructed by applying the singular manifold method. Based on the obtained Lax representation, the Darboux transformation （DT） is constructed. The first iterated solution, second iterated solution and a special N-soliton solution with an arbitrary function are derived with the resulting DT. Relevant properties are graphically illustrated, which might be helpful to understanding the propagation processes for ocean waves in shallow water.

关键词： (2+1)-dimensional generalization of shallow water wave equation singular manifold method Laxpair Darboux transformation symbolic computation

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A New (2+1)-Dimensional KdV Equation and Its Localized Structures

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Communications in Theoretical Physics 2010年第11期 863-865页

作者：彭彦泽 School of Mathematics and Statistics Wuhan University

A new （2＋1）-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms... 详细信息

关键词： (2+1)-dimensional KdV equation Lax pair generating technique singular manifold method

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