New families of travelling wave solutions for Boussinesq–Burgers equation and ()-dimensional Kadomtsev–Petviashvili equation

2007 ◽  
Vol 366 (4-5) ◽  
pp. 411-421 ◽  
Author(s):  
Liang Gao ◽  
Wei Xu ◽  
Yaning Tang ◽  
Gaofeng Meng
Keyword(s):  
Burgers Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation

Bright soliton solutions, power series solutions and travelling wave solutions of a (3+1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili equation

2018 ◽  
Vol 32 (06) ◽  
pp. 1850082
Author(s):  
Ding Guo ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Bright Soliton ◽  
Travelling Wave Solutions ◽  
Series Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Power Series Solutions ◽  
De Vries

In this paper, we consider the (3[Formula: see text]+[Formula: see text]1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdV-KP) equation, which can be used to describe the nonlinear waves in plasma physics and fluid dynamics. By using solitary wave ansatz in the form of sech[Formula: see text] function and a direct integrating way, we construct the exact bright soliton solutions and the travelling wave solutions of the equation, respectively. Moreover, we obtain its power series solutions with the convergence analysis. It is hoped that our results can provide the richer dynamical behavior of the KdV-type and KP-type equations.

Travelling-wave solutions to the Korteweg-de Vries-Burgers equation

1985 ◽  
Vol 101 (3-4) ◽  
pp. 207-226 ◽  
Author(s):  
J. L. Bona ◽  
M. E. Schonbek
Keyword(s):  
Burgers Equation ◽  
Travelling Wave ◽  
Singular Limit ◽  
Travelling Wave Solutions ◽  
Qualitative Properties ◽  
Wave Solutions ◽  
De Vries ◽  
Limiting Behaviour ◽  
Image Position

SynopsisThe existence and certain qualitative properties of travelling-wave solutions to the Korteweg-de Vries-Burgers equation,are established. The limiting behaviour of these waves, when ε tends to zero and when δ tends to zero is examined together with a singular limit wherein both ε and δ tend to zero.

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