The nonlinear Schrödinger equation on the half-line with Neumann boundary conditions

DOI10.1016/J.APNUM.2018.09.018zbMath1420.35358OpenAlexW2894971733MaRDI QIDQ2000080

Dionyssios Mantzavinos, Fangchi Yan, A. Alexandrou Himonas

Publication date: 27 June 2019

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.09.018

zbMATH Keywords

nonlinear Schrödinger equationunified transform method\(L^2\)-boundedness of Laplace transforminitial-boundary value problem with Neumann dataintegrable equations and solitonswell-posedness in Sobolev spaces on the half-line

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Laplace transform (44A10) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (9)

The interior-boundary Strichartz estimate for the Schrödinger equation on the half-line revisited ⋮ A higher dispersion KdV equation on the half-line ⋮ Stochastic nonlinear Schrödinger equation on half-line with boundary noise ⋮ Integral representations for the double-diffusivity system on the half-line ⋮ Critical exponent for global existence of solutions to the Schrödinger equation with a nonlinear boundary condition ⋮ Construction of solutions and asymptotics for the defocusing NLS with periodic boundary data ⋮ The nonlinear Schrödinger equation on the half-line with a Robin boundary condition ⋮ Inhomogeneous Neumann-boundary value problem for one dimensional nonlinear Schrödinger equations via factorization techniques ⋮ The Neumann and Robin problems for the Korteweg–de Vries equation on the half-line

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity properties of the cubic nonlinear Schrödinger equation on the half line
• Dispersive blow-up for nonlinear Schrödinger equations revisited
• The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line.
• On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Nonhomogeneous boundary-value problems for one-dimensional nonlinear Schrödinger equations
• On the ill-posedness of some canonical dispersive equations.
• Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm
• The ``good Boussinesq equation on the half-line
• A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane
• The Korteweg–de Vries equation on the half-line
• The nonlinear Schrödinger equation on the half-line
• Water waves, nonlinear Schrödinger equations and their solutions
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• A Unified Approach to Boundary Value Problems
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Solution of the forced nonlinear schrödinger (nls) equation using pde techniques
• Nonlinear modulation of gravity waves: a rigorous approach
• A unified transform method for solving linear and certain nonlinear PDEs
• THE GENERALIZED KORTEWEG–DE VRIES EQUATION ON THE HALF LINE
• Microlocal dispersive smoothing for the Schrödinger equation
• The Initial-Boundary Value Problem for the Korteweg–de Vries Equation
• The Propagation of Nonlinear Wave Envelopes
• Wave Instabilities
• An inhomogeneous boundary value problem for nonlinear Schrödinger equations

This page was built for publication: The nonlinear Schrödinger equation on the half-line with Neumann boundary conditions