On a class of nonintegrable equations in 1+1 dimensions with factorized associated linear operators

Publisher Website
Google Scholar
Abstract
We consider a class of nonintegrable nonlinear equations with powerlike nonlinearities KN, ∂xKN (K being the solutions and N≥2, N integer) building explicitly their exponential type bisolitons. The denominators of the bisolitons have no soliton couplings, and the linear differential operators of the linear part of the equations are factorized operators. We extend our study to a larger class of nonlinearities: polynomial nonlinearities which are linear combinations of powerlike nonlinearities. We study the two extreme possibilities. Either the bisoliton is specific of a mixed nonlinearity, not being a solution of any component nonlinearity, or the bisoliton is common to all components. Different properties occur depending whether the components are KN or ∂xKN. For KN nonlinearities, in order to understand the origin of the factorization of the linear operators, we give a criterion which is easily checked at an almost entirely linear level of constraints. We conjecture that all possible bisolitons are of the type studied here. Finally for KN and ∂xKN we enlarge the class of bisolitons found in previous works.