Non-stationary Solitary Wave Solution for Damped Forced Kadomtsev–Petviashvili Equation in a Magnetized Dusty Plasma with q-Nonextensive Velocity Distributed Electron

2021 ◽  
Vol 7 (6) ◽  
Author(s):  
Santanu Raut ◽  
Ashim Roy ◽  
Kajal Kumar Mondal ◽  
Prasanta Chatterjee ◽  
Naresh M. Chadha
Keyword(s):  
Solitary Wave ◽  
Dusty Plasma ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Magnetized Dusty Plasma ◽  
Petviashvili Equation

Solitary wave solutions, lump solutions and interactional solutions to the (2+1)-dimensional potential Kadomstev–Petviashvili equation

2019 ◽  
Vol 34 (04) ◽  
pp. 2050055
Author(s):  
Jiang-Su Geng ◽  
Hai-Qiang Zhang
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Lump Solution ◽  
Bilinear Method ◽  
Elastic Interactions ◽  
Petviashvili Equation ◽  
Pkp Equation ◽  
Hirota Bilinear

In this paper, the [Formula: see text]-solitary wave solution to the (2[Formula: see text]+[Formula: see text]1)-dimensional potential Kadomstev–Petviashvili (PKP) equation is obtained with the Hirota bilinear method. Via the limit technique of long wave, the [Formula: see text]-lump solution can be derived from resulting [Formula: see text]-solitary wave solution. In addition, interactional solutions consisting of lumps and solitary waves for the PKP equation are obtained, which can describe elastic interactions of lumps and solitary waves. These results are illustrated by graphics of several sample examples.

scholarly journals Joint Application of Bilinear Operator and F-Expansion Method for (2+1)-Dimensional Kadomtsev-Petviashvili Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shaolin Li ◽  
Yinghui He ◽  
Yao Long
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Expansion Method ◽  
Traveling Wave Solution ◽  
Bilinear Operator ◽  
Test Function ◽  
Joint Application ◽  
Petviashvili Equation

The bilinear operator and F-expansion method are applied jointly to study (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation. An exact cusped solitary wave solution is obtained by using the extended single-soliton test function and its mechanical feature which blows up periodically in finite time for cusped solitary wave is investigated. By constructing the extended double-soliton test function, a new type of exact traveling wave solution describing the assimilation of solitary wave and periodic traveling wave is also presented. Our results validate the effectiveness for joint application of the bilinear operator and F-expansion method.

scholarly journals Solitary wave solution for a class of dusty plasma

2014 ◽  
Vol 63 (11) ◽  
pp. 110203
Author(s):  
Ouyang Cheng ◽  
Yao Jing-Sun ◽  
Shi Lan-Fang ◽  
Mo Jia-Qi
Keyword(s):  
Solitary Wave ◽  
Dusty Plasma ◽  
Wave Solution ◽  
Solitary Wave Solution

scholarly journals Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoxiao Zheng ◽  
Yadong Shang ◽  
Yong Huang
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Constant Coefficient ◽  
Wave Solution ◽  
Integral Method ◽  
Solitary Wave Solution ◽  
First Integral ◽  
Mkdv Equation ◽  
Variable Coefficients ◽  
First Integral Method

This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used to establish abundant exact explicit solution of VC-mKdV equation. By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.

A regularized model for strongly nonlinear internal solitary waves

2009 ◽  
Vol 629 ◽  
pp. 73-85 ◽  
Author(s):  
WOOYOUNG CHOI ◽  
RICARDO BARROS ◽  
TAE-CHANG JO
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Solution ◽  
Wave Amplitude ◽  
Solitary Wave Solution ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Strongly Nonlinear ◽  
Regularized Model

The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis that internal solitary waves are locally stable to perturbations of arbitrary wavelengths if the wave amplitudes are smaller than a critical value. For a wide range of depth and density ratios pertinent to oceanic conditions, the critical wave amplitude is close to the maximum wave amplitude and the regularized model is therefore expected to be applicable to the strongly nonlinear regime. The regularized model is solved numerically using a finite-difference method and its numerical solutions support the results of our linear stability analysis. It is also shown that the solitary wave solution of the regularized model, found numerically using a time-dependent numerical model, is close to the solitary wave solution of the original model, confirming that the two models are asymptotically equivalent.

New Solitary Wave Solution for the Boussinesq Wave Equation Using the Semi-Inverse Method and the Exp-Function Method

2009 ◽  
Vol 64 (11) ◽  
pp. 709-712 ◽  
Author(s):  
Wenjun Liu
Keyword(s):  
Wave Equation ◽  
Variational Principle ◽  
Solitary Wave ◽  
Wave Solution ◽  
Variational Formulation ◽  
Function Method ◽  
Inverse Method ◽  
Solitary Wave Solution ◽  
Solitary Solutions

Using the semi-inverse method, a variational formulation is established for the Boussinesq wave equation. Based on the obtained variational principle, solitary solutions in the sech-function and expfunction forms are obtained

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