Stability of solitary waves for derivative nonlinear Schrödinger equation
From MaRDI portal
Publication:850176
DOI10.1016/j.anihpc.2005.09.003zbMath1104.35050OpenAlexW2048408704MaRDI QIDQ850176
Publication date: 15 November 2006
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIHPC_2006__23_5_753_0
Stability in context of PDEs (35B35) Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)
Related Items (42)
A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation ⋮ Orbital stability of solitary waves for Kundu equation ⋮ Existence and stability of standing waves for coupled derivative Schrödinger equations ⋮ Construction of multi-solitons and multi kink-solitons of derivative nonlinear Schrödinger equations ⋮ Instability of degenerate solitons for nonlinear Schrödinger equations with derivative ⋮ Global well-posedness for the derivative nonlinear Schrödinger equation ⋮ Solitary waves for nonlinear Schrödinger equation with derivative ⋮ Orbital stability of solitary waves for derivative nonlinear Schrödinger equation ⋮ Stability of solitary waves for a generalized derivative nonlinear Schrödinger equation ⋮ Existence of normalized solutions for the coupled elliptic system with quadratic nonlinearity ⋮ Standing waves of coupled Schrödinger equations with quadratic interactions from Raman amplification in a plasma ⋮ Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations ⋮ Stability of the sum of two solitary waves for (gDNLS) in the energy space ⋮ A Fourier analysis approach to elliptic equations with critical potentials and nonlinear derivative terms ⋮ Liouville type theorems and periodic solutions for the nonhomogeneous parabolic systems ⋮ Traveling waves for a nonlinear Schrödinger system with quadratic interaction ⋮ Virial functional and dynamics for nonlinear Schrödinger equations of local interactions ⋮ Instability of the solitary waves for the generalized derivative nonlinear Schrödinger equation in the degenerate case ⋮ Admissible boundary values for the Gerdjikov-Ivanov equation with asymptotically time-periodic boundary data ⋮ 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 ⋮ Orbital stability of a two parameter family of solitary waves for a fourth order nonlinear Schrödinger type equation ⋮ Instability of solitary wave solutions for the nonlinear Schrödinger equation of derivative type in degenerate case ⋮ Solitary waves for coupled nonlinear elliptic system with nonhomogeneous nonlinearities ⋮ Stability of the traveling waves for the derivative Schrödinger equation in the energy space ⋮ On the stability of periodic waves for the cubic derivative NLS and the quintic NLS ⋮ Orbital stability of solitary waves for generalized derivative nonlinear Schrödinger equations in the endpoint case ⋮ Instability of solitary wave solutions for derivative nonlinear Schrödinger equation in endpoint case ⋮ Soliton resolution for the derivative nonlinear Schrödinger equation ⋮ Potential well theory for the derivative nonlinear Schrödinger equation ⋮ On the derivative nonlinear Schrödinger equation on the half line with Robin boundary condition ⋮ Modulational instability of periodic standing waves in the derivative NLS equation ⋮ Orbital stability of standing waves for nonlinear fractional Schrödinger equation with unbounded potential ⋮ Microscopic conservation laws for the derivative nonlinear Schrödinger equation ⋮ On a class of derivative Nonlinear Schrödinger-type equations in two spatial dimensions ⋮ The derivative nonlinear Schrödinger equation: Global well-posedness and soliton resolution ⋮ 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 ⋮ Schrödinger systems with quadratic interactions ⋮ Exact solutions of a generalized variant of the derivative nonlinear Schrödinger equation in a Scarff II external potential and their stability properties ⋮ Nonlinear stability of multi-solitons for the Hirota equation ⋮ Stability of algebraic solitons for nonlinear Schrödinger equations of derivative type: variational approach
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonlinear Schrödinger equations and sharp interpolation estimates
- On the lowest eigenvalue of the Laplacian for the intersection of two domains
- Stable standing waves of nonlinear Klein-Gordon equations
- Stability theory of solitary waves in the presence of symmetry. II
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- Stability of Coulomb systems with magnetic fields. I: The one-electron atom
- Instability of nonlinear bound states
- Stability theory of solitary waves in the presence of symmetry. I
- On the derivative nonlinear Schrödinger equation
- Stability of standing waves for the generalized Davey-Stewartson system
- Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity
- Asymptotic profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity
- Stability and instability of standing waves for the generalized Davey- Stewartson system
- Stability and instability of standing waves for one dimensional nonlinear Schrödinger equations with double power nonlinearity
- Orbital stability of solitary waves for the nonlinear derivative Schrödinger equation
- Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations
- Modified Nonlinear Schrödinger Equation for Alfvén Waves Propagating along the Magnetic Field in Cold Plasmas
- A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
- Lyapunov stability of ground states of nonlinear dispersive evolution equations
- 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
This page was built for publication: Stability of solitary waves for derivative nonlinear Schrödinger equation
