Integrable nonlocal derivative nonlinear Schrödinger equations
Mark J. Ablowitz, Xu‐Dan Luo, Ziad H. Musslimani, Yi Zhu
Abstract
Abstract Integrable standard and nonlocal derivative nonlinear Schrödinger equations are investigated. The direct and inverse scattering are constructed for these equations; included are both the Riemann–Hilbert and Gel’fand–Levitan–Marchenko approaches and soliton solutions. As a typical application, it is shown how these derivative NLS equations can be obtained as asymptotic limits from a nonlinear Klein–Gordon equation.
Topics & Concepts
Integrable systemMathematicsInverse scattering transformDerivative (finance)Nonlinear systemInverse scattering problemQuantum inverse scattering methodMathematical physicsMathematical analysisSolitonNonlinear Schrödinger equationInverseLax pairRiemann–Hilbert problemInverse problemSchrödinger equationPhysicsQuantum mechanicsGeometryEconomicsFinancial economicsBoundary value problemNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum Mechanics and Non-Hermitian Physics