Inverse scattering transforms for non-local reverse-space matrix non-linear Schrödinger equations
Wen‐Xiu Ma, Yehui Huang, Fudong Wang
Abstract
The aim of the paper is to explore non-local reverse-space matrix non-linear Schrödinger equations and their inverse scattering transforms. Riemann–Hilbert problems are formulated to analyse the inverse scattering problems, and the Sokhotski–Plemelj formula is used to determine Gelfand–Levitan–Marchenko-type integral equations for generalised matrix Jost solutions. Soliton solutions are constructed through the reflectionless transforms associated with poles of the Riemann–Hilbert problems.
Topics & Concepts
Inverse scattering transformInverse scattering problemMathematicsRiemann–Hilbert problemScatteringMatrix (chemical analysis)InverseQuantum inverse scattering methodMathematical analysisSolitonSpace (punctuation)Inverse problemPhysicsNonlinear systemQuantum mechanicsGeometryComputer scienceMaterials scienceComposite materialBoundary value problemOperating systemNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum Mechanics and Non-Hermitian Physics