Open AccessLie symmetries of Generalized Equal Width wave equations
Author(s) -
Mobeen Munir,
Muhammad Athar,
Sakhi G. Sarwar,
Wasfı Shatanawi
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021705
Subject(s) - mathematics , ordinary differential equation , differential equation , homogeneous space , sine gordon equation , infinitesimal , symmetry (geometry) , mathematical analysis , first order partial differential equation , partial differential equation , wave equation , riccati equation , ode , mathematical physics , physics , nonlinear system , quantum mechanics , geometry , soliton
Lie symmetry analysis of differential equations proves to be a powerful tool to solve or atleast to reduce the order and non-linearity of the equation. The present article focuses on the solution of Generalized Equal Width wave (GEW) equation using Lie group theory. Over the years, different solution methods have been tried for GEW but Lie symmetry analysis has not been done yet. At first, we obtain the infinitesimal generators, commutation table and adjoint table of Generalized Equal Width wave (GEW) equation. After this, we find the one dimensional optimal system. Then we reduce GEW equation into non-linear ordinary differential equation (ODE) by using the Lie symmetry method. This transformed equation can take us to the solution of GEW equation by different methods. After this, we get the travelling wave solution of GEW equation by using the Sine-cosine method. We also give graphs of some solutions of this equation.