Matrix Integrable Fourth-Order Nonlinear Schrödinger Equations and Their Exact Soliton Solutions
Wen‐Xiu Ma
Abstract
We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz–Kaup–Newell–Segur matrix eigenvalue problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding reflectionless Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and formulate their soliton solutions via those reflectionless Riemann–Hilbert problems. Soliton solutions are computed for three illustrative examples of scalar and two-component integrable fourth-order nonlinear Schrödinger equations.
Topics & Concepts
Integrable systemEigenvalues and eigenvectorsScalar (mathematics)SolitonMathematical physicsNonlinear systemMatrix (chemical analysis)Nonlinear Schrödinger equationMathematicsOrder (exchange)PhysicsMathematical analysisQuantum mechanicsComposite materialFinanceGeometryMaterials scienceEconomicsNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum Mechanics and Non-Hermitian Physics