Nonlinear modulation of periodic waves in the cylindrical Gardner equation

Aslanova, Gunay; Ahmetolan, Semra; Demırcı, Ali

doi:10.1103/physreve.102.052215

Cited by 6 publications

(1 citation statement)

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“…Aslanova et al [21] studied the propagating characteristic of dispersive shock waves through the cylindrical Gardner equation, which is derived from the ð2 + 1Þ-dimensional KP-mKP equation by using a similarity reduction transformation. Boateng et al [22] derived some trigonometric and hyperbolic trigonometric analytical solution of ð2 + 1Þ-dimensional KP-mKP equation employing the modified extended direct algebraic method.…”

Section: Introductionmentioning

confidence: 99%

The Classification of the Exact Single Travelling Wave Solutions to the Constant Coefficient KP-mKP Equation Employing Complete Discrimination System for Polynomial Method

Sarkar

Raut²,

Mali

2022

Computational and Mathematical Methods

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The purpose of this article is to explore different types of solutions for the Kadomtsev-Petviashvili-modified Kadomtsev-Petviashvili (KP-mKP) equation which is termed as KP-Gardner equation, extensively used to model strong nonlinear internal waves in ( 1 + 2 )-dimensions on the stratified ocean shelf. This evolution equation is also used to describe weakly nonlinear shallow-water wave and dispersive interracial waves traveling in a mildly rotating channel with slowly varying topography. Introducing Liu’s approach regarding the complete discrimination system for polynomial and the trial equation technique, a set of new solutions to the KP-mKP equation containing Jacobi elliptic function have been derived. It is found that these analytical solutions numerically exhibit different nonlinear structures such as solitary waves, shock waves, and periodic wave profiles. The reliability and effectiveness are confirmed from the numerical graphs of the solutions. Finally, the existence and validity of the various topological structures of the solutions are confirmed from the phase portrait of the dynamical system. Based on this investigation, it is confirmed that the method is not only suited for obtaining the classification of the solutions but also for qualitative analysis, which means that it can also be extended to other fields of application.

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Section: Introductionmentioning

confidence: 99%