Well-posedness and existence of bound states for a coupled Schrödinger-gKdV system
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Publication:988157
DOI10.1016/j.na.2010.06.049zbMath1194.35405OpenAlexW2029035696MaRDI QIDQ988157
Filipe Oliveira, M. S. Figueira, João-Paulo Dias
Publication date: 26 August 2010
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.na.2010.06.049
KdV equations (Korteweg-de Vries equations) (35Q53) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55)
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Cites Work
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- Vanishing viscosity with short wave-long wave interactions for multi-D scalar conservation laws
- Existence of bound states for the coupled Schrödinger-KdV system with cubic nonlinearity
- Small solutions to nonlinear Schrödinger equations
- Nonlinear scalar field equations. I: Existence of a ground state
- Existence of local strong solutions for a quasilinear Benney system
- Vanishing viscosity with short wave-long wave interactions for systems of conservation laws
- Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
- Nonlinear small data scattering for the generalized Korteweg-de Vries equation
- Bound and ground states of coupled nonlinear Schrödinger equations
- Asymptotic stability of solitons of the gKdV equations with general nonlinearity
- Well-posedness for the Schrödinger-Korteweg-de Vries system
- EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS
- Stability and instability of solitary waves of Korteweg-de Vries type
- Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
- A General Theory for Interactions Between Short and Long Waves
- Asymptotic Solutions of the Korteweg-deVries Equation
- Well-posedness of the cauchy problem for the long wave-short wave resonance equations
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions
- On the Ill-Posedness of the IVP for the Generalized Korteweg-De Vries and Nonlinear Schrödinger Equations
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