Auto-Backlund transformations and new exact travelling wave solutions of Kadomtsev-Petviashvili equation for nonlinear dust acoustic solitary waves in dust plasmas with variable dust charge and two temperature ions

2014 ◽  
Vol 8 ◽  
pp. 789-810
Author(s):  
R.S. Ibrahim ◽  
A. R. Seadawy ◽  
H.A. Abd El-Hamed
Keyword(s):  
Solitary Waves ◽  
Travelling Wave ◽  
Bäcklund Transformations ◽  
Travelling Wave Solutions ◽  
Dust Charge ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Dust Acoustic Solitary Waves ◽  
Dust Acoustic ◽  
Two Temperature

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.

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