The purpose of this study is to investigate the deeper characteristics of the system of shallow
water wave equations that is used to model the turbulence in the atmosphere and oceans …

In this paper, we concern ourselves with the nonlinear Kadomtsev–Petviashvili equation
(KP) with a competing dispersion effect. First we examine the integrability of governing …

In this work, we present a new two-mode version to the complex Hirota equation. This new
model arises in many applications in the field of optics, communications and other …

A new two-mode version of the generalized Zakharov-Kuznetsov equation is derived using
Korsunsky's method. This dynamical model describes the propagation of two-wave solitons …

In this paper we communicated with three different ansatze methods including the tanh-
expansion method, the rational sine–cosine method and the Kudryashov-expansion method …

Recently, a new family of nonlinear physical models under the name of dual-mode nonlinear
equations has been arisen. Several real-valued dual-mode equations associated with well …

Abstract In this study, the (2+ 1)-dimensional combined Korteweg–de Vries and modified
Korteweg–de Vries equation has been considered for the first time. Firstly, we check the …

A numerical investigation of the coupled viscous Burgers' equation for very large Reynolds
numbers do not exist in the literature. Coupled viscous Burgers' equations are solved …

In this paper, we establish a new nonlinear equation which is called the two-mode Korteweg–
de Vries–Burgers equation (TMKdV–BE). The new equation describes the propagation of …

In this work, Kudryashov's equation with third-order dispersion and fourth-order dispersion
was studied via Lie symmetry analysis. First, similarity transformation helps us to converted …