A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation

DOI10.2140/apde.2017.10.1149zbMath1371.35271arXiv1610.00267OpenAlexW2609429061MaRDI QIDQ2362324

Takahisa Inui, Noriyoshi Fukaya, Masayuki Hayashi

Publication date: 7 July 2017

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.00267

zbMATH Keywords

variational structureglobal existencegeneralized derivative nonlinear Schrödinger equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (22)

Construction of multi-solitons and multi kink-solitons of derivative nonlinear Schrödinger equations ⋮ Instability of degenerate solitons for nonlinear Schrödinger equations with derivative ⋮ Solitary waves for nonlinear Schrödinger equation with derivative ⋮ Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations ⋮ On the well-posedness problem for the derivative nonlinear Schrödinger equation ⋮ Prescribed solutions of a nonlinear fractional Schrödinger system with quadratic interaction ⋮ Traveling waves for a nonlinear Schrödinger system with quadratic interaction ⋮ Growth bound and nonlinear smoothing for the periodic derivative nonlinear Schrödinger equation ⋮ Instability of the solitary waves for the generalized derivative nonlinear Schrödinger equation in the degenerate case ⋮ Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities ⋮ Global well-posedness for the derivative non-linear Schrödinger equation ⋮ Instability of algebraic standing waves for nonlinear Schrödinger equations with double power nonlinearities ⋮ On a class of solutions to the generalized derivative Schrödinger equations. II ⋮ Instability of solitary wave solutions for the nonlinear Schrödinger equation of derivative type in degenerate case ⋮ Orbital stability of solitary waves for generalized derivative nonlinear Schrödinger equations in the endpoint case ⋮ Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line ⋮ Remarks on blow-up criteria for the derivative nonlinear Schrödinger equation under the optimal threshold setting ⋮ Potential well theory for the derivative nonlinear Schrödinger equation ⋮ Modulational instability of periodic standing waves in the derivative NLS equation ⋮ On a class of solutions to the generalized derivative Schrödinger equations ⋮ Long-period limit of exact periodic traveling wave solutions for the derivative nonlinear Schrödinger equation ⋮ Stability of algebraic solitons for nonlinear Schrödinger equations of derivative type: variational approach

Cites Work

• Unnamed Item
• Well-posedness for a generalized derivative nonlinear Schrödinger equation
• Stability of solitary waves for a generalized derivative nonlinear Schrödinger equation
• Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems
• Global well-posedness on the derivative nonlinear Schrödinger equation
• Global well-posedness for the derivative nonlinear Schrödinger equation in \(H^{\frac {1}{2}} (\mathbb{R})\)
• Stability of the traveling waves for the derivative Schrödinger equation in the energy space
• Global well-posedness for Schrödinger equation with derivative in \(H^{\frac {1}{2}} (\mathbb R)\)
• Nonlinear scalar field equations. I: Existence of a ground state
• On the lowest eigenvalue of the Laplacian for the intersection of two domains
• Stability of solitary waves for derivative nonlinear Schrödinger equation
• Stability theory of solitary waves in the presence of symmetry. II
• Stability theory of solitary waves in the presence of symmetry. I
• On the derivative nonlinear Schrödinger equation
• Saddle points and instability of nonlinear hyperbolic equations
• Remarks on nonlinear Schrödinger equations in one space dimension
• Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity
• Orbital stability of solitary waves for the nonlinear derivative Schrödinger equation
• Existence and uniqueness of solution for a generalized nonlinear derivative Schrödinger equation
• Well-posedness for one-dimensional derivative nonlinear Schrödinger equations
• Global well-posedness for the nonlinear Schrödinger equation with derivative in energy space
• On global solution of nonlinear hyperbolic equations
• Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations
• Global Well-Posedness for Schrödinger Equations with Derivative
• Modified Nonlinear Schrödinger Equation for Alfvén Waves Propagating along the Magnetic Field in Cold Plasmas
• Multi-Solitary Waves for the Nonlinear Klein-Gordon Equation
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• The initial value problem for the derivative nonlinear Schrödinger equation in the energy space
• Finite Energy Solutions of Nonlinear Schrödinger Equations of Derivative Type
• On the nonlinear Schrodinger equations of derivative type
• A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative

This page was built for publication: A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation