Multiple residual symmetries and soliton-cnoidal wave interaction solution of the $$(2+1)$$-dimensional negative-order modified Calogero–Bogoyavlenskii–Schiff equation

2020 ◽  
Vol 135 (1) ◽  
Author(s):  
Wenguang Cheng ◽  
Deqin Qiu ◽  
Tianzhou Xu
Keyword(s):  
Wave Interaction ◽  
Cnoidal Wave ◽  
Interaction Solution ◽  
Negative Order

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.

Exact soliton solutions for the interaction of few-cycle-pulse with nonlinear medium

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640013 ◽  
Author(s):  
Bang-Xing Guo ◽  
Ji Lin
Keyword(s):  
Nonlinear Medium ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Expansion Method ◽  
Periodic Wave ◽  
Interaction Solution ◽  
Coupled Equations ◽  
Waves Interaction ◽  
The One ◽  
Cycle Pulse

We study the Panilevé property of the coupled equations describing the interaction of few-cycle-pulse with nonlinear medium. And we use the consistent tanh expansion (CTE) method to search for exact interaction soliton solutions of the coupled equations. Many interaction solutions are obtained, such as the one kink-one periodic wave interaction solution, one kink-two periodic waves interaction solution, one kink-one dipole soliton interaction solution, one kink-two dipole solitons interaction solution, and one kink-soliton-one periodic wave interaction solution. We also obtain the kink–kink interaction by using Painlevé truncated expansion method.

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