Painleve analysis, Auto-Backlund transformation and new exact solutions for improved modied KdV equation

Abstract

Improved modified Korteweg-de Vries (IMKdV) equation is shown to be non-integrable using Painlevé analysis. Exact travelling wave solutions are obtained using auto-Bäcklund transformation and Linearized transformation.

Auto-Backlund transformations and New Exact Soliton Solutions of KdV Equation for Nonlinear Dust Acoustic Solitary Waves in Dust Plasma with Variable Dust Charge

“…Since the general solutions (48) are well known to us, then substituting α 0 , α i , α −i and γ and the general solutions (48) into (47), we have the traveling wave solutions of the given NPDE. For KdV equation (23), to transform it to ODE using the wave variable χ = lξ − ρτ , so these equation became…”

“…where ψ(τ ) is a differentiable function, f (χ, η) is a function to be determined later and φ 0 be the special (old) solution of KdV equation (23). In the following analysis, we will stay with the following conditions…”

“…Substituting from equation (43) into equation (25), we have, the new exact soliton solution of KdV equation (23) in the form…”

“…For KdV equation (23), to transform it to ODE using the wave variable χ = ρτ − lξ , so these equation became…”

“…We use the reductive perturbation technique to derive a KdV equation. would like to use the homogeneous balance method [15,16] to construct an auto-Bäcklund transformation (BT) [17][18][19][20][21][22][23] , new exact soliton solutions of KdV equation are obtained and we have applied the modifiedǴ G expansion method [24][25][26][27][28][29][30][31], the sine-cosine expansion method, the sinh-coshine expansion method ,and the sech-tanh expansion method [33,[37][38][39][40][41] and to obtain a new travelling wave solutions of KdV equation. The paper is organized as follows :This introduction in Section 1.…”