The unified method: I. Nonlinearizable problems on the half-line
From MaRDI portal
Publication:2890761
DOI10.1088/1751-8113/45/19/195201zbMath1256.35044arXiv1109.4935OpenAlexW3104325835MaRDI QIDQ2890761
Jonatan Lenells, Athanassios S. Fokas
Publication date: 12 June 2012
Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1109.4935
Riemann-Hilbert problemDirichlet boundary conditionNeumann boundary conditioninitial boundary value problemintegrable PDE
KdV equations (Korteweg-de Vries equations) (35Q53) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)
Related Items (68)
A two-component modified Korteweg–de Vries equation: Riemann–Hilbert problem and multi-soliton solutions ⋮ Initial-boundary problems for the vector modified Korteweg-de Vries equation via Fokas unified transform method ⋮ The inverse scattering transform and soliton solutions of a combined modified Korteweg-de Vries equation ⋮ The Ablowitz–Ladik system on a finite set of integers ⋮ Inverse scattering transforms for non-local reverse-space matrix non-linear Schrödinger equations ⋮ The Korteweg-de Vries equation on the half-line with Robin and Neumann data in low regularity spaces ⋮ Riemann-Hilbert problems of a six-component mKdV system and its soliton solutions ⋮ A higher dispersion KdV equation on the half-line ⋮ Initial-boundary value problems for the general coupled nonlinear Schrödinger equation on the interval via the Fokas method ⋮ Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval ⋮ Riemann-Hilbert problems and \(N\)-soliton solutions for a coupled mKdV system ⋮ Initial-boundary value problems of the coupled modified Korteweg–de Vries equation on the half-line via the Fokas method ⋮ The unified transform method to the high-order nonlinear Schrödinger equation with periodic initial condition ⋮ Inverse scattering and soliton solutions of high-order matrix nonlinear Schrödinger equation ⋮ A coupled complex mKdV equation and its N-soliton solutions via the Riemann-Hilbert approach ⋮ Integrability and high-order localized waves of the (4 + 1)-dimensional nonlinear evolution equation ⋮ Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane ⋮ Boundary behavior for the heat equation on the half‐line ⋮ The defocusing nonlinear Schrödinger equation with \(t\)-periodic data: new exact solutions ⋮ Initial-boundary value problems for the two-component complex modified Korteweg-de Vries equation on the interval ⋮ The Majda-Biello system on the half-line ⋮ The partial-rogue ripple solutions of nonlocal Kadomtsev-Petviashvili equation ⋮ \(N\)-(soliton, breather) interactions for general multi-component third-fifth-order mKdV equations via Riemann-Hilbert method ⋮ Revised Riemann-Hilbert problem for the derivative nonlinear Schrödinger equation: vanishing boundary condition ⋮ Initial-Boundary Value Problem for Two-Component Gerdjikov–Ivanov Equation with 3 × 3 Lax Pair on Half-Line ⋮ Reverse-time type nonlocal Sasa–Satsuma equation and its soliton solutions ⋮ Riemann-Hilbert approach and \(N\)-soliton solutions for a new two-component Sasa-Satsuma equation ⋮ Sasa-Satsuma type matrix integrable hierarchies and their Riemann-Hilbert problems and soliton solutions ⋮ Multi-soliton solutions for a higher-order coupled nonlinear Schrödinger system in an optical fiber via Riemann-Hilbert approach ⋮ Initial-boundary value problems associated with the Ablowitz-Ladik system ⋮ Unnamed Item ⋮ Initial-boundary value problems for integrable evolution equations with \(3\times 3\) Lax pairs ⋮ Boundary value problems for the elliptic sine-Gordon equation in a semi-strip ⋮ Riemann-Hilbert approach for a coherently-coupled nonlinear Schrödinger system associated with a \(4\times 4\) matrix spectral problem ⋮ Riemann-Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions ⋮ The Fokas method for integrable evolution equations on a time-dependent interval ⋮ Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies ⋮ The nonlinear steepest descent approach for long time behavior of the two-component coupled Sasa-Satsuma equation with a \(5 \times 5\) Lax pair ⋮ Inverse scattering and \(N\)-triple-pole soliton and breather solutions of the focusing nonlinear Schrödinger hierarchy with nonzero boundary conditions ⋮ Admissible boundary values for the defocusing nonlinear Schrödinger equation with asymptotically time-periodic data ⋮ Asymptotics of solutions to a fifth-order modified Korteweg–de Vries equation in the quarter plane ⋮ An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line ⋮ Some open problems in random matrix theory and the theory of integrable systems. II ⋮ The Fokas Method: The Dirichlet to Neumann Map for the Sine‐Gordon Equation ⋮ Application of the Riemann-Hilbert method to the vector modified Korteweg-de Vries equation ⋮ A necessary and sufficient condition for the solvability of the nonlinear Schrödinger equation on a finite interval ⋮ Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 × 4 Lax pair on a finite interval ⋮ The hyperbolic Ernst equation in a triangular domain ⋮ Initial-Boundary Value Problem for Integrable Nonlinear Evolution Equation with 3 × 3 Lax Pairs on the Interval ⋮ Initial-Boundary Value Problems for the Coupled Nonlinear Schrödinger Equation on the Half-Line ⋮ The massive Thirring system in the quarter plane ⋮ Inverse scattering for nonlocal reverse-space multicomponent nonlinear Schrödinger equations ⋮ The KdV Equation on the Half-Line: Time-Periodicity and Mass Transport ⋮ Riemann-Hilbert problems and soliton solutions for a multi-component cubic-quintic nonlinear Schrödinger equation ⋮ The Modified Korteweg-de Vries Equation on the Half-Line with a Sine-Wave as Dirichlet Datum ⋮ A Perturbative Approach for the Asymptotic Evaluation of the Neumann Value Corresponding to the Dirichlet Datum of a Single Periodic Exponential for the NLS ⋮ The Elliptic Sinh-Gordon Equation in the Quarter Plane ⋮ Initial-boundary value problem for the two-component nonlinear Schrödinger equation on the half-line ⋮ The modified Korteweg-de Vries equation on the quarter plane with t-periodic data ⋮ The unified transform method for the Sasa–Satsuma equation on the half-line ⋮ The Riemann-Hilbert Approach and $N$-Soliton Solutions of a Four-Component Nonlinear Schrödinger Equation ⋮ Initial-boundary value problems for a reaction-diffusion equation ⋮ Riemann-Hilbert Approach and N-Soliton Solutions For Three-Component Coupled Hirota Equations ⋮ The Ablowitz-Ladik system on a graph ⋮ Initial‐Boundary Value Problems for the Defocusing Nonlinear Schrödinger Equation in the Semiclassical Limit ⋮ Soliton Theory and Hankel Operators ⋮ Extended water wave systems of Boussinesq equations on a finite interval: theory and numerical analysis ⋮ On the inverse scattering method for integrable PDEs on a star graph
This page was built for publication: The unified method: I. Nonlinearizable problems on the half-line
