Construction and separability of nonlinear soliton integrable couplings

TL;DR

This paper introduces a natural method for constructing integrable extensions of soliton systems through algebra modifications, providing a general solution form and a decoupling procedure applicable to various coupled systems.

Contribution

It presents a novel algebra-based approach for creating integrable soliton couplings and derives a general solution and decoupling method for these systems.

Findings

Constructed integrable extensions via algebra modifications.

Derived a general solution form for coupled systems.

Developed a decoupling procedure applicable to multiple systems.

Abstract

A very natural construction of integrable extensions of soliton systems is presented. The extension is made on the level of evolution equations by a modification of the algebra of dynamical fields. The paper is motivated by recent works of Wen-Xiu Ma et al. (Comp. Math. Appl. 60 (2010) 2601, Appl. Math. Comp. 217 (2011) 7238), where new class of soliton systems, being nonlinear integrable couplings, was introduced. The general form of solutions of the considered class of coupled systems is described. Moreover, the decoupling procedure is derived, which is also applicable to several other coupling systems from the literature.