The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the
following steps:(1) Lax representation [L, M]= 0;(2) construction of fundamental analytic …

Dressing Method for the Degasperis–Procesi Equation - Constantin - 2017 - Studies in
Applied Mathematics - Wiley Online Library Skip to Article Content Skip to Article …

This paper presents the functional expansion approach as a generalized method for finding
traveling wave solutions of various nonlinear partial differential equations. The approach …

In this paper, we show that complete integrability is preserved in a multicomponent
differential-difference Volterra system with branched dispersion relation. Using the Hirota …

We analyze several types of soliton solutions to a family of Tzitzeica equations. To this end
we use two methods for deriving the soliton solutions: the dressing method and Hirota …

The present paper is dedicated to integrable models with Mikhailov reduction groups $
G_R\simeq\mathbb {D} _h. $ Their Lax representation allows us to prove, that their solution …

This paper uses the attached flow method for solving nonlinear second-order differential
equations of the reaction–diffusion type. The key steps of the method consist of the …

We start with the Lax representation for the Kaup-Kupersschmidt equation (KKE). We We
outline the deep relation between the scalar Lax operator and the matrix Lax operators …

Solitons and bifurcations for the generalized Tzitzéica type equation are studied by using the
theory of dynamical systems and Hamilton function. With the help of Maple and bifurcation …

We have derived the hierarchy of soliton equations associated with the untwisted affine Kac-
Moody algebra D 4 (1) by calculating the corresponding recursion operators. The …