Consistent Riccati expansion solvable classification and soliton-cnoidal wave interaction solutions for an extended Korteweg-de Vries equation

Cheng, Wenguang; Xu, Tianzhou

doi:10.1016/j.cjph.2018.09.032

Cited by 9 publications

(6 citation statements)

References 47 publications

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“…For example, we just take a simple solution of Eq. (1) is obtained by substituting above u, ψ, φ into (15).…”

Section: Localization Of the Nonlocal Symmetrymentioning

confidence: 99%

“…Recently, the nonlocal symmetry method [9,10] which related to the infinitesimal forms of lax pairs or Bäcklund transformations has been widely applied to construct interaction solutions of some nonlinear systems. Lou et al [11][12][13][14][15][16] have pointed out that there is a close relationship between Painlevé analysis and nonlocal symmetries, i.e. the last variable introduced in the localization process of nonlocal symmetry must satisfy the Schwartzian form of the equation, and this theory greatly simplifies the process of constructing exact solutions to closed systems.…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalized variable coefficient shallow water wave equation

Xin

Zhang

Xia

et al. 2019

Applied Mathematics Letters

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“…For example, we just take a simple solution of Eq. (1) is obtained by substituting above u, ψ, φ into (15).…”

Section: Localization Of the Nonlocal Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalized variable coefficient shallow water wave equation

Xin

Zhang

Xia

et al. 2019

Applied Mathematics Letters

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“…ese interaction excitations cannot be obtained by the direct Lie point symmetry method. Recently, different types of excitations are valid by using the symmetry reductions related to nonlocal symmetry and a consistent tanh expansion (CTE) method [20][21][22][23][24][25][26][27][28]. e CTE method can be investigated not only for various different types of excitations but also for an integrable property of the nonlinear systems, including the supersymmetric extension of the nonlinear systems [29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

CTE Solvability, Nonlocal Symmetry, and Interaction Solutions of Coupled Integrable Dispersionless System

Ren

Liu

et al. 2022

Complexity

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The consistent tanh expansion (CTE) method is successfully applied to the coupled integrable dispersionless (CID) system. A nonauto-Bäcklund transformation (BT) theorem includes two fields f and v 1 is obtained by using the CTE method. One obtains the consistent condition in the nonauto-BT theorem by means of the relation between the fields f and v 1 . The CID system possesses the CTE solvability property by some detailed analysis. Many interactions between one soliton and multiple resonant solitons, and between one soliton and cnoidal waves are generated by using the nonauto-BT theorem. The types of bright and gray two front waves are shown by some figures. In the meanwhile, the nonlocal symmetry is obtained by the truncated Painlevé method and the Möbious invariant form. The initial value problem and an auto-BT are constructed by the localization procedure.

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“…In this paper, we focus on the following (2 + 1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff (KdV-CBS) equation [27] [28] [29].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for (2 + 1)-Dimensional KdV-Calogero-Bogoyavlenkskii-Schiff Equation via Symbolic Computation

Li¹,

Chaolu²

2020

JAMP

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This paper constructs exact solutions for the (2 + 1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff equation with the help of symbolic computation. By means of the truncated Painlev expansion, the (2 + 1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff equation can be written as a trilinear equation, through the trilinear-linear equation, we can obtain the explicit representation of exact solutions for the (2 + 1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff equation. We have depicted the profiles of the exact solutions by presenting their three-dimensional plots and the corresponding density plots.

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Consistent Riccati expansion solvable classification and soliton-cnoidal wave interaction solutions for an extended Korteweg-de Vries equation

Cited by 9 publications

References 47 publications

Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalized variable coefficient shallow water wave equation

Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalized variable coefficient shallow water wave equation

CTE Solvability, Nonlocal Symmetry, and Interaction Solutions of Coupled Integrable Dispersionless System

Exact Solutions for (2 + 1)-Dimensional KdV-Calogero-Bogoyavlenkskii-Schiff Equation via Symbolic Computation

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