Inverse scattering and soliton solutions of nonlocal reverse-spacetime nonlinear Schrödinger equations
Wen‐Xiu Ma
Abstract
The paper presents nonlocal reverse-spacetime PT-symmetric multicomponent nonlinear Schrödinger (NLS) equations under a specific nonlocal group reduction, and generates their inverse scattering transforms and soliton solutions by the Riemann-Hilbert technique. The Sokhotski-Plemelj formula is used to determine solutions to a class of associated Riemann-Hilbert problems and transform the systems that generalized Jost solutions need to satisfy. A formulation of solutions is developed for the Riemann-Hilbert problems associated with the reflectionless transforms, and the corresponding soliton solutions are constructed for the presented nonlocal reverse-spacetime PT-symmetric NLS equations.
Topics & Concepts
SpacetimeInverse scattering problemRiemann hypothesisRiemann–Hilbert problemSolitonInverse scattering transformNonlinear systemMathematical physicsHilbert spaceMathematical analysisInverseMathematicsPhysicsInverse problemQuantum mechanicsGeometryBoundary value problemNonlinear Waves and SolitonsQuantum Mechanics and Non-Hermitian PhysicsNonlinear Photonic Systems