The classification of single travelling wave solutions to the Camassa–Holm–Degasperis–Procesi equation for some values of the convective parameter

Wang, Chunyan; Guan, Jiang; Bao-Yan, Wang

doi:10.1007/s12043-011-0098-z

Cited by 10 publications

(5 citation statements)

References 12 publications

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“…It is found that if a NLEE can be turned into an integral form then all possible exact solutions can be derived by this CDSPM [58]. Recently, this method has been used successively for solving many NLEEs [59][60][61][62]. Fan et al applied this method to find all possible exact travelling wave solutions to the generalized Pochhammer-Chree equation [63].…”

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%

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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“…[4] In the previous equation, the RHS represents dispersion and the value of the balance parameter was taken as b = 2. The Camassa-Holm-Degasperis-Procesi (CHDP) was introduced by Degasperis and Procesi [4] , also studied in [5]…”

Section: Introductionmentioning

confidence: 99%

“…into the equation of the coefficient corresponding to (ψ′(ξ)) −5 leads to, Solving the previous equations with the dispersion relation(5) leads to the following:…”

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confidence: 99%

Untitled

2021

AJMS

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In this work, we study the Camassa Holm Degasperis Procesi equation through solving it by three different methods which are the factorization technique, the Cole-Hopf method, and the Schwarzian derivatives method, plus studying the stability of the system through the Phase Portrait method. Illustrations of the solution are presented using symbolic software which shows different pattern formations.

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“…By Liu's method, many nonlinear partial differential equations have been solved. For example, Wang and Li [10] used Liu's method and other methods to investigate the single and multi-solitary solutions to some nonlinear evolution equations; Wang et al [11] obtained the classification of traveling wave solutions to CH-DP equation; and, Fan [12] gave the classification of the single traveling wave solutions to the generalized equal width equation, and so on.…”

Section: Introductionmentioning

confidence: 99%

On the exact solutions to the long—short-wave interaction system

Fan¹,

Fan²,

Li³

2014

Chinese Phys. B

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The classification of single travelling wave solutions to the Camassa–Holm–Degasperis–Procesi equation for some values of the convective parameter

Abstract: By the complete discrimination system for the polynomial, we give the classification of single travelling wave solutions to the Camassa-Holm-Degasperis-Procesi equation for some values of the convective parameter.

Cited by 10 publications

References 12 publications

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

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

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On the exact solutions to the long—short-wave interaction system

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