Abstract
New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics.
Highlights
It is well known that nonlinear complex physical phenomena are related to nonlinear partial differential equations (NLPDEs), which are implicated in many fields from physics to biology, chemistry, mechanics, engineering, etc
This article is organised as follows: In Section 2, we give the description of a new extended generalized Kudryashov method for the first time
From (22) we deduce that Eq (1) has the dark soliton solution α0 β0
Summary
It is well known that nonlinear complex physical phenomena are related to nonlinear partial differential equations (NLPDEs), which are implicated in many fields from physics to biology, chemistry, mechanics, engineering, etc. The objective of this article is to use a new extended generalized Kudryashov method, for the first time, to construct new exact solutions of the following three nonlinear partial differential equations (PDEs). (I) The (1 + 1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity [17]: iEt + aExt + bExx +. E(x, t) is the complex valued wave profile for the (1 + 1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity. The coefficients a and b represent the improved term that introduces stability to the NLS equation and the usual group velocity dispersion (GVD), respectively. The parameters α and λ represent the intermodal dispersion and the self-steepening perturbation term, respectively. This article is organised as follows: In Section 2, we give the description of a new extended generalized Kudryashov method for the first time. Eqs. (1), (2) and (3) are not discussed before using the proposed method obtained
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