Existence of bound states for the coupled Schrödinger-KdV system with cubic nonlinearity

DOI10.1016/j.crma.2010.09.018zbMath1205.35247OpenAlexW2038437738MaRDI QIDQ609374

Filipe Oliveira, M. S. Figueira, João-Paulo Dias

Publication date: 30 November 2010

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2010.09.018

zbMATH Keywords

minimization problemcoupled Schrödinger-KdV systemsmooth positive bound states

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Variational methods applied to PDEs (35A15) Positive solutions to PDEs (35B09)

Related Items (15)

Convergence of a numerical scheme for a coupled Schrödinger-KdV system ⋮ Infinitely many solitary waves due to the second-harmonic generation in quadratic media ⋮ On the existence of bound and ground states for some coupled nonlinear Schrödinger-Korteweg-de Vries equations ⋮ High-order compact finite difference scheme with two conserving invariants for the coupled nonlinear Schrödinger–KdV equations ⋮ Standing waves of coupled Schrödinger equations with quadratic interactions from Raman amplification in a plasma ⋮ Ground state solution for Schrödinger-KdV system with periodic potential ⋮ A higher order system of some coupled nonlinear Schrödinger and Korteweg-de Vries equations ⋮ Uniqueness of positive solutions to some coupled cooperative variational elliptic systems ⋮ Well-posedness and existence of bound states for a coupled Schrödinger-gKdV system ⋮ Ground state solutions for a non-autonomous nonlinear Schrödinger-KdV system ⋮ Existence and bifurcation of nontrivial solutions for the coupled nonlinear Schrödinger-Korteweg-de Vries system ⋮ Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system ⋮ On soliton solutions to a class of Schrödinger-K𝐝V systems ⋮ On Long Time Behavior of Solutions of the Schrödinger--Korteweg--de Vries System ⋮ Existence of bound and ground states for a system of coupled nonlinear Schrödinger-KdV equations

Cites Work

• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Bound and ground states of coupled nonlinear Schrödinger equations
• Well-posedness for the Schrödinger-Korteweg-de Vries system
• Existence and stability of ground-state solutions of a Schrödinger—KdV system
• Existence and evenness of solitary-wave solutions for an equation of short and long dispersive waves
• Stability of stationary states for the coupled Klein — Gordon — Schrödinger equations

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