Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion—advection equation with variable coefficients

2014 ◽  
Vol 23 (3) ◽  
pp. 030201 ◽  
Author(s):  
Vikas Kumar ◽  
R. K. Gupta ◽  
Ram Jiwari
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Group Analysis ◽  
Traveling Wave Solutions ◽  
Variable Coefficients ◽  
Advection Equation ◽  
Lie Group Analysis ◽  
Wave Solutions ◽  
Dimensional Diffusion

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 New non-traveling wave solutions for (3+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation

2021 ◽  
Vol 6 (3) ◽  
pp. 2996-3008
Author(s):  
Yuanqing Xu ◽  
◽  
Xiaoxiao Zheng ◽  
Jie Xin ◽  
◽  
...  
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Variable Coefficients ◽  
Wave Solutions ◽  
Dimensional Variable

Symmetry reductions and rational non-traveling wave solutions for the (2+1)-D Ablowitz-Kaup-Newell-Segur equation

2016 ◽  
Vol 26 (8) ◽  
pp. 2331-2339 ◽  
Author(s):  
Xiao-rong Kang ◽  
Xian Daquan
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Group Method ◽  
Content Type ◽  
Lie Group Method ◽  
Localized Structures ◽  
Wave Solutions ◽  
Akns Equation

Purpose The purpose of this paper is to find out some new rational non-traveling wave solutions and to study localized structures for (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation. Design/methodology/approach Along with some special transformations, the Lie group method and the rational function method are applied to the (2+1)-dimensional AKNS equation. Findings Some new non-traveling wave solutions are obtained, including generalized rational solutions with two arbitrary functions of time variable. Research limitations/implications As a typical nonlinear evolution equation, some dynamical behaviors are also discussed. Originality/value With the help of the Lie group method, special transformations and the rational function method, new non-traveling wave solutions are derived for the AKNS equation by Maple software. These results are much useful for investigating some new localized structures and the interaction of waves in high-dimensional models, and enrich dynamical features of solutions for the higher dimensional systems.

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