Soliton solutions to the time-dependent coupled KdV–Burgers’ equation

Abstract

In this article, the authors apply the Lie symmetry approach and the modified (G /G)-expansion method for seeking the solutions of time-dependent coupled KdV-Burgers equation. Using suitable similarity transformations, the time-dependent coupled KdV-Burgers equation is reduced to a system of nonlinear ordinary differential equations. Further, the reduced system of nonlinear ordinary differential equations for the coupled KdV equation is solved with the help of the modified (G /G)-expansion method to obtain soliton solutions which are expressed by hyperbolic functions, trigonometric functions, and rational functions.

Time-fractional (2+1)-dimensional navier-stokes equations: similarity reduction and exact solutions for one-parameter lie group of rotations

“…It is easy to see that all these infinitesimals contain all the physical properties of the dependent variables of the governed equation (1). The general formula which modulates these infinitesimals mathematically can be defined as follows (for more details, see [1][2][3][4][5][6][7])…”

“…As we know Lie symmetry analysis [1][2][3][4][5][6][7][8][9][10][11][12][13] is a powerful and flexible tool for developing algorithms for analyzing nonlinear differential equations. R E Boisvert et al [14] applied this powerful tool to the classical integer order Navier-Stokes equations.…”

Lie symmetry analysis for complex soliton solutions of coupled complex short pulse equation

“…In this section, equivalent to each subalgebras, we obtained the reduced system of nonlinear ordinary differential equations 29–31 in the form of similarity variable ' ξ ' and the corresponding dependent variables ϒ 1 , Ζ 1 and ϒ 2 , Ζ 2 . Further, new complex soliton solutions of the coupled complex short pulse Equation are obtained by solving the reduced ordinary differential equations.…”

Notes on Local and Nonlocal Intuitionistic Fuzzy Fractional Boundary Value Problems with Caputo Fractional Derivatives

“…Ngo et al, in [7], proved the existence and uniqueness results of solutions for initial value problem under fuzzy Caputo-Katugampola fractional derivatives. For many basic works related to the nonlinear ordinary differential equations and the fuzzy fractional differential equations, we refer the readers to [8][9][10][11][12][13] and references therein.…”