On a Riemann-Hilbert problem for the Fokas-Lenells equation

DOI10.1016/j.aml.2018.07.027zbMath1501.37072OpenAlexW2883861304MaRDI QIDQ1726493

Jian Xu, Liping Ai

Publication date: 20 February 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2018.07.027

zbMATH Keywords

Riemann-Hilbert probleminitial value problemFokas-Lenells equationnegative-order Lax pair

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (16)

Fokas-Lenells equation: three types of Darboux transformation and multi-soliton solutions ⋮ A coupled complex mKdV equation and its N-soliton solutions via the Riemann-Hilbert approach ⋮ Riemann-Hilbert approach to the focusing and defocusing nonlocal derivative nonlinear Schrödinger equation with step-like initial data ⋮ On the Riemann–Hilbert problem of a generalized derivative nonlinear Schrödinger equation ⋮ The Fokas–Lenells equations: Bilinear approach ⋮ Nonautonomous dynamics of local and nonlocal Fokas–Lenells models ⋮ Riemann–Hilbert problem for the Fokas–Lenells equation in the presence of high-order discrete spectrum with non-vanishing boundary conditions ⋮ Explicit Nth order solutions of Fokas–Lenells equation based on revised Riemann–Hilbert approach ⋮ Riemann-Hilbert problems and soliton solutions for a generalized coupled Sasa-Satsuma equation ⋮ On the Poisson structure and action-angle variables for the Fokas-Lenells equation ⋮ Revised Riemann-Hilbert problem for the derivative nonlinear Schrödinger equation: vanishing boundary condition ⋮ The Fokas-Lenells equation on the line: global well-posedness with solitons ⋮ Riemann–Hilbert approach to the focusing and defocusing nonlocal complex modified Korteweg–de Vries equation with step-like initial data ⋮ On the Riemann-Hilbert problem for the mixed Chen-Lee-Liu derivative nonlinear Schrödinger equation ⋮ Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions ⋮ Long-time asymptotics for the focusing Fokas-Lenells equation in the solitonic region of space-time

Cites Work

• Dressing for a novel integrable generalization of the nonlinear Schrödinger equation
• On a class of physically important integrable equations
• Long-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: without solitons
• A direct method of solution for the Fokas–Lenells derivative nonlinear Schrödinger equation: I. Bright soliton solutions
• Lattice representation and dark solitons of the Fokas–Lenells equation
• A direct method of solution for the Fokas–Lenells derivative nonlinear Schrödinger equation: II. Dark soliton solutions
• Exactly Solvable Model for Nonlinear Pulse Propagation in Optical Fibers
• An integrable generalization of the nonlinear Schrödinger equation on the half-line and solitons
• Then-order rogue waves of Fokas-Lenells equation
• On a novel integrable generalization of the nonlinear Schrödinger equation

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