Traveling wave solutions of a generalized modified Kadomtsev–Petviashvili equation

2004 ◽  
Vol 45 (6) ◽  
pp. 2181-2187 ◽  
Author(s):  
H. W. Schürmann ◽  
V. S. Serov
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation

scholarly journals Lie Group Method for Solving the Negative-Order Kadomtsev–Petviashvili Equation (nKP)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 224
Author(s):  
Ghaylen Laouini ◽  
Amr M. Amin ◽  
Mohamed Moustafa
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Invariant Solution ◽  
Traveling Wave Solutions ◽  
Group Method ◽  
Lie Group Method ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Negative Order ◽  
Petviashvili Equation

A comprehensive study of the negative-order Kadomtsev–Petviashvili (nKP) partial differential equation by Lie group method has been presented. Initially the infinitesimal generators and symmetry reduction, which were obtained by applying the Lie group method on the negative-order Kadomtsev–Petviashvili equation, have been used for constructing the reduced equations. In particular, the traveling wave solutions for the negative-order KP equation have been derived from the reduced equations as an invariant solution. Finally, the extended improved (G′/G) method and the extended tanh method are described and applied in constructing new explicit expressions for the traveling wave solutions. Many new and more general exact solutions are obtained.

scholarly journals Exact Traveling Wave Solutions and Bifurcation of a Generalized (3+1)-Dimensional Time-Fractional Camassa-Holm-Kadomtsev-Petviashvili Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zhigang Liu ◽  
Kelei Zhang ◽  
Mengyuan Li
Keyword(s):  
Traveling Wave ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Phase Portraits ◽  
Wave System ◽  
Bifurcation Method ◽  
Exact Traveling Wave Solutions ◽  
Fractional Complex Transform ◽  
Wave Solutions ◽  
Petviashvili Equation

In this paper, we study the (3+1)-dimensional time-fractional Camassa-Holm-Kadomtsev-Petviashvili equation with a conformable fractional derivative. By the fractional complex transform and the bifurcation method for dynamical systems, we investigate the dynamical behavior and bifurcation of solutions of the traveling wave system and seek all possible exact traveling wave solutions of the equation. Furthermore, the phase portraits of the dynamical system and the remarkable features of the solutions are demonstrated via interesting figures.

scholarly journals Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation

2000 ◽  
Vol 24 (6) ◽  
pp. 371-377 ◽  
Author(s):  
Kenneth L. Jones ◽  
Xiaogui He ◽  
Yunkai Chen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Integral Equations ◽  
Traveling Wave ◽  
Vries Equation ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
De Vries ◽  
Periodic Traveling Wave

This paper is concerned with periodic traveling wave solutions of the forced generalized nearly concentric Korteweg-de Vries equation in the form of(uη+u/(2η)+[f(u)]ξ+uξξξ)ξ+uθθ/η2=h0. The authors first convert this equation into a forced generalized Kadomtsev-Petviashvili equation,(ut+[f(u)]x+uxxx)x+uyy=h0, and then to a nonlinear ordinary differential equation with periodic boundary conditions. An equivalent relationship between the ordinary differential equation and nonlinear integral equations with symmetric kernels is established by using the Green's function method. The integral representations generate compact operators in a Banach space of real-valued continuous functions. The Schauder's fixed point theorem is then used to prove the existence of nonconstant solutions to the integral equations. Therefore, the existence of periodic traveling wave solutions to the forced generalized KP equation, and hence the nearly concentric KdV equation, is proved.

scholarly journals Analysis of Stability of Traveling Wave for Kadomtsev-Petviashvili Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Jun Liu ◽  
Xi Liu ◽  
Gui Mu ◽  
Chunyan Zhu ◽  
Jie Fu
Keyword(s):  
Lyapunov Function ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Uniform Boundedness ◽  
Wave Transformation ◽  
Kp Equation ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Analysis Of Stability

This paper presents the boundedness and uniform boundedness of traveling wave solutions for the Kadomtsev-Petviashvili (KP) equation. They are discussed by means of a traveling wave transformation and Lyapunov function.

scholarly journals Lie Symmetry Analysis, Traveling Wave Solutions, and Conservation Laws to the (3 + 1)-Dimensional Generalized B-Type Kadomtsev-Petviashvili Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Huizhang Yang ◽  
Wei Liu ◽  
Yunmei Zhao
Keyword(s):  
Conservation Laws ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Bkp Equation

In this paper, the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili(BKP) equation is studied applying Lie symmetry analysis. We apply the Lie symmetry method to the (3 + 1)-dimensional generalized BKP equation and derive its symmetry reductions. Based on these symmetry reductions, some exact traveling wave solutions are obtained by using the tanh method and Kudryashov method. Finally, the conservation laws to the (3 + 1)-dimensional generalized BKP equation are presented by invoking the multiplier method.

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