CRE solvability and soliton-cnoidal wave interaction solutions of the dissipative (2+1)-dimensional AKNS equation

AbstractThe truncated Painlevé method is developed to obtain the nonlocal residual symmetry and the Bäcklund transformation for the (2+1)-dimensional KdV–mKdV equation. The residual symmetry is localised after embedding the (2+1)-dimensional KdV–mKdV equation to an enlarged one. The symmetry group transformation of the enlarged system is computed. Furthermore, the (2+1)-dimensional KdV–mKdV equation is proved to be consistent Riccati expansion (CRE) solvable. The soliton–cnoidal wave interaction solution in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral is obtained by using the consistent tanh expansion (CTE) method, which is a special form of CRE.

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

Chinese Journal of Physics ◽

10.1016/j.cjph.2018.09.032 ◽

2018 ◽

Vol 56 (6) ◽

pp. 2753-2759 ◽

Cited By ~ 4

Author(s):

Wenguang Cheng ◽

Tianzhou Xu

Keyword(s):

Vries Equation ◽

Wave Interaction ◽

Cnoidal Wave ◽

Interaction Solutions ◽

De Vries ◽

Consistent Riccati Expansion

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N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation

Modern Physics Letters B ◽

10.1142/s0217984921502778 ◽

2021 ◽

pp. 2150277

Author(s):

Hongcai Ma ◽

Qiaoxin Cheng ◽

Aiping Deng

Keyword(s):

Dynamic Behavior ◽

Soliton Solution ◽

Soliton Solutions ◽

Wave Interaction ◽

Bilinear Transformation ◽

Interaction Solution ◽

Interaction Solutions ◽

Ytsf Equation ◽

Line Soliton

[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the interaction solution among period soliton and two line solitons, or the interaction solution for two period solitons or two lump solitons via taking specific constraints from four soliton solutions. Finally, some images of the results are drawn, and their dynamic behavior is analyzed.

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Investigation of Interaction Solutions for Modified Korteweg-de Vries Equation by Consistent Riccati Expansion Method

Mathematical Problems in Engineering ◽

10.1155/2019/9535294 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8

Author(s):

Jin-Fu Liang ◽

Xun Wang

Keyword(s):

Vries Equation ◽

Soliton Solutions ◽

Wave Interaction ◽

Expansion Method ◽

Periodic Wave ◽

Mkdv Equation ◽

Jacobi Elliptic Function ◽

Interaction Solutions ◽

De Vries ◽

Consistent Riccati Expansion

A consistent Riccati expansion (CRE) method is proposed for obtaining interaction solutions to the modified Korteweg-de Vries (mKdV) equation. Using the CRE method, it is shown that interaction solutions such as the soliton-tangent (or soliton-cotangent) wave cannot be constructed for the mKdV equation. More importantly, exact soliton-cnoidal periodic wave interaction solutions are presented. While soliton-cnoidal interaction solutions were found to degenerate to special resonant soliton solutions for the values of modulus (n) closer to one (upper bound of modulus) in the Jacobi elliptic function, a normal kink-shaped soliton was observed for values of n closer to zero (lower bound).

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