Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane

DOI10.1111/sapm.12089zbMath1335.35217arXiv1501.05285OpenAlexW2963686097MaRDI QIDQ2793204

Jonatan Lenells

Publication date: 15 March 2016

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

Full work available at URL: https://arxiv.org/abs/1501.05285

zbMATH Keywords

Riemann-Hilbert problemmKdV equationnonlinear Fourier transforms

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Numerical methods for discrete and fast Fourier transforms (65T50) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (8)

Long-time asymptotics for the Kundu–Eckhaus equation on the half-line ⋮ Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane ⋮ Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line ⋮ Long‐time asymptotics to the defocusing generalized nonlinear Schrödinger equation with the decaying initial value problem ⋮ Construction of solutions and asymptotics for the defocusing NLS with periodic boundary data ⋮ The Nonlinear Steepest Descent Method: Asymptotics for Initial-Boundary Value Problems ⋮ The initial-boundary value for the combined Schrödinger and Gerdjikov-Ivanov equation on the half-line via the Riemann-Hilbert approach ⋮ On the spectral problem associated with the time-periodic nonlinear Schrödinger equation

Cites Work

• Unnamed Item
• Unnamed Item
• Riemann-Hilbert approach to the elastodynamic equation. I
• The Kadomtsev-Petviashvili II equation on the half-plane
• Boundary value problems for the \(N\)-wave interaction equations
• The Degasperis-Procesi equation on the half-line
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• The defocusing nonlinear Schrödinger equation with \(t\)-periodic data: new exact solutions
• Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane
• The derivative nonlinear Schrödinger equation on the half-line
• Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line
• On the solvability of Painlevé II and IV
• The modified KdV equation on a finite interval.
• Matrix Riemann-Hilbert problems with jumps across Carleson contours
• The three-wave equation on the half-line
• Integrable nonlinear evolution equations on the half-line
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• The generalized Dirichlet to Neumann map for the KdV equation on the half-line
• Integrable nonlinear evolution equations on a finite interval
• A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane
• The unified transform method for the Sasa–Satsuma equation on the half-line
• Addendum to ‘On the Dirichlet to Neumann problem for the 1-dimensional cubic NLS equation on the half-line’
• Explicit Soliton Asymptotics for the Nonlinear Schrödinger Equation on the Half-Line
• The Korteweg–de Vries Equation, Posed in a Quarter-Plane
• The Riemann-Hilbert Formalism For Certain Linear and Nonlinear Integrable PDEs
• Decaying Long-Time Asymptotics for the Focusing NLS Equation with Periodic Boundary Condition
• Inverse scattering on the line
• A unified transform method for solving linear and certain nonlinear PDEs
• The Riemann–Hilbert Problem and Inverse Scattering
• THE GENERALIZED KORTEWEG–DE VRIES EQUATION ON THE HALF LINE
• THE mKdV EQUATION ON THE HALF-LINE
• Semiclassical nonlinear Schrödinger on the half line
• Initial‐Boundary Value Problems for the Defocusing Nonlinear Schrödinger Equation in the Semiclassical Limit
• The Initial-Boundary Value Problem for the Korteweg–de Vries Equation
• The elliptic sine-Gordon equation in a half plane

This page was built for publication: Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane