Classification of Solitary Wave Bifurcations in Generalized Nonlinear Schrödinger Equations
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Publication:4648287
DOI10.1111/j.1467-9590.2012.00549.xzbMath1250.35163arXiv1203.5148OpenAlexW1742515310MaRDI QIDQ4648287
Publication date: 8 November 2012
Published in: Studies in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1203.5148
NLS equations (nonlinear Schrödinger equations) (35Q55) Bifurcations in context of PDEs (35B32) Soliton solutions (35C08)
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Cites Work
- Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials
- Trapped bright matter-wave solitons in the presence of localized inhomogeneities
- Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
- Classification of the solitary waves in coupled nonlinear Schrödinger equations
- Geometric analysis of bifurcation and symmetry breaking in a Gross-Pitaevskii equation
- Spontaneous symmetry breaking in photonic lattices: theory and experiment
- Solitary-wave and multi-pulsed traveling-wave solutions of boussinesq systems
- From non-local gap solitary waves to bound states in periodic media
- Nonlinear Waves in Integrable and Nonintegrable Systems
- Travelling solitons in the externally driven nonlinear Schrödinger equation
- Symmetry-Breaking Bifurcation in Nonlinear Schrödinger/Gross–Pitaevskii Equations
- Homoclinic snaking: Structure and stability
- On asymmetric gravity–capillary solitary waves
- Normal Forms and Unfoldings for Local Dynamical Systems
- Weakly Nonlocal Solitary Waves in a Singularly Perturbed Nonlinear Schrödinger Equation
- Three Is a Crowd: Solitary Waves in Photorefractive Media with Three Potential Wells
- On the formation of bound states by interacting nonlocal solitary waves
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