Explicit soliton–cnoidal wave interaction solutions for the (2+1)-dimensional negative-order breaking soliton equation

2018 ◽  
Vol 30 (1) ◽  
pp. 54-64 ◽  
Author(s):  
Jinxi Fei ◽  
Weiping Cao
Keyword(s):  
Wave Interaction ◽  
Cnoidal Wave ◽  
Soliton Equation ◽  
Interaction Solutions ◽  
Negative Order

Residual Symmetry and Explicit Soliton–Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV–mKdV Equation

2016 ◽  
Vol 71 (4) ◽  
pp. 351-356 ◽  
Author(s):  
Wenguang Cheng ◽  
Biao Li
Keyword(s):  
Elliptic Integral ◽  
Wave Interaction ◽  
Elliptic Functions ◽  
Mkdv Equation ◽  
Jacobi Elliptic Functions ◽  
Cnoidal Wave ◽  
Residual Symmetry ◽  
The Third ◽  
Interaction Solutions ◽  
Consistent Riccati Expansion

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.

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

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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