In the study of nonlinear physics, the search of new exact solutions of nonlinear evolution equations (NEEs) is one of the most important problems. Various methods for obtaining exact solutions to NEEs have been proposed, such as the Lie group method of infinitesimal transformations [1], the nonclassical Lie group method [2], the Clarkson and Kruskal direct method (CK) [3 – 5], the conditional ...

The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multisymplectic formulation of this equation gives an explicit relation between the parameters for transverse instability when the transverse wave number is small. The Evans func...

In this paper, we employ the modified simple equation method to find the exact traveling wave solutions involving parameters of nonlinear evolution equations via the (1+1)dimensional generalized shallow water-wave equation and the(2+1)-dimensional KdV-Burgers equation. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave sol...

There has been a large amount of work aimed at understanding the stability of nonlinear dispersive equations that support solitary wave solutions[20, 7, 3, 6, 19, 29, 28, 30, 35, 36]. Much of this work relies on understanding detailed properties of the spectrum of the operator obtained by linearizing the flow around the solitary wave. These spectral properties, in turn, have important implicati...

The (2+1)-dimensional “universal” variable separation formula (Tang, Lou and Zhang, Physical Review E 66, 046601 (2002)) is extended to a more general form for some (2+1)-dimensional integrable systems. Various independent arbitrary functions have been included in the extended formula. Starting from the universal formula and its extended form, a new type of solitons, foldons, is studied both an...

We present a method to prove nonlinear instability of solitary waves in dispersive models. Two examples are analyzed: we prove the nonlinear long time instability of the KdV solitary wave (with respect to periodic transverse perturbations) under a KP-I flow and the transverse nonlinear instability of solitary waves for the cubic nonlinear Schrödinger equation.

We have worked on (2+1)-dimensional dissipative long wave system (DLWS) and Date-Jimbo-Kashiwara-Miwa (DJKM) equation. applied GKM, which has been obtained by generalizing the Kudryashov method, to (2+1)- dimensional DLWS DJKM Thus, we got some new soliton solutions of handled plotted 2D 3D surfaces these acquired results using Wolfram Mathematica 12. Then, shown validity solutions.

We consider a U(1)-invariant nonlinear Klein-Gordon equation in dimension n ≥ 1, self-interacting via the mean field mechanism. We analyze the long-time asymptotics of finite energy solutions and prove that, under certain generic assumptions, each solution converges as t →±∞ to the two-dimensional set of all “nonlinear eigenfunctions” of the form φ(x)e−iωt . This global attraction is caused by ...

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equati...