Multisoliton generation in inhomogeneous nonlinear Schrödinger and Heisenberg spin systems

Abstract

Certain linearly Χ-dependent and circularly symmetric generalized nonlinear Schrödinger equations and their geometrically/gauge equivalent Heisenberg spin systems are integrable through the inverse scattering formalism. In this paper, using the concept of gauge transformation of the associated linear eigenvalue problems, we construct the Backlund transformations and use them to generate multisoliton solutions, especially explicit two-soliton solutions for these systems. The construction procedure is purely algebraic and it depends only on the eigenfunction of the vacuum linear system.