Optimal system, invariance analysis of fourth-Order nonlinear ablowitz-Kaup-Newell-Segur water wave dynamical equation using lie symmetry approach

2021 ◽  
Vol 404 ◽  
pp. 126230
Author(s):  
Munesh Devi ◽  
Shalini Yadav ◽  
Rajan Arora
Keyword(s):  
Fourth Order ◽  
Water Wave ◽  
Dynamical Equation ◽  
Lie Symmetry ◽  
Optimal System ◽  
Symmetry Approach ◽  
Lie Symmetry Approach

Lie symmetry analysis, optimal system and conservation law of a generalized (2+1)-dimensional Hirota–Satsuma–Ito equation

2021 ◽  
Author(s):  
Sheng-Nan Guan ◽  
Guang-Mei Wei ◽  
Qi Li
Keyword(s):  
Soliton Solutions ◽  
Adjoint Representation ◽  
Similarity Solutions ◽  
Lie Symmetry ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
Symmetry Approach ◽  
Lie Symmetry Approach ◽  
Ito Equation

In this paper, a generalized (2+1)-dimensional Hirota–Satsuma–Ito (GHSI) equation is investigated using Lie symmetry approach. Infinitesimal generators and symmetry groups of this equation are presented, and the optimal system is given with adjoint representation. Based on the optimal system, some symmetry reductions are performed and some similarity solutions are provided, including soliton solutions and periodic solutions. With Lagrangian, it is shown that the GHSI equation is nonlinearly self-adjoint. By means of the Lie point symmetries and nonlinear self-adjointness, the conservation laws are constructed. Furthermore, some physically meaningful solutions are illustrated graphically with suitable choices of parameters.

Soliton Solutions, Conservation Laws, and Reductions of Certain Classes of NonlinearWave Equations

2012 ◽  
Vol 67 (10-11) ◽  
pp. 613-620 ◽  
Author(s):  
Richard Morris ◽  
Abdul Hamid Kar ◽  
Abhinandan Chowdhury ◽  
Anjan Biswas
Keyword(s):  
Conservation Laws ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Lie Symmetry ◽  
Nonlinear Wave Equations ◽  
Conserved Quantities ◽  
Symmetry Approach ◽  
Lie Symmetry Approach

In this paper, the soliton solutions and the corresponding conservation laws of a few nonlinear wave equations will be obtained. The Hunter-Saxton equation, the improved Korteweg-de Vries equation, and other such equations will be considered. The Lie symmetry approach will be utilized to extract the conserved densities of these equations. The soliton solutions will be used to obtain the conserved quantities of these equations.

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