Bifurcation and Stability of Travelling Waves in Self-focusing Planar Waveguides
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Publication:4932332
DOI10.1515/ans-2010-0207zbMath1204.35152OpenAlexW2512764406MaRDI QIDQ4932332
Publication date: 1 October 2010
Published in: Advanced Nonlinear Studies (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/ans-2010-0207
Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Bifurcations in context of PDEs (35B32) Traveling wave solutions (35C07) Quantum dots, waveguides, ratchets, etc. (81Q37)
Related Items (15)
On stability and instability of standing waves for the inhomogeneous fractional Schrödinger equation ⋮ Blowup of \(H^1\) solutions for a class of the focusing inhomogeneous nonlinear Schrödinger equation ⋮ Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation ⋮ On the critical norm concentration for the inhomogeneous nonlinear Schrödinger equation ⋮ Finite time/infinite time blow-up behaviors for the inhomogeneous nonlinear Schrödinger equation ⋮ Global bifurcation for asymptotically linear Schrödinger equations ⋮ Threshold Solutions for the Intercritical Inhomogeneous NLS ⋮ Scattering of radial solutions to the inhomogeneous nonlinear Schrödinger equation ⋮ Local well-posedness for the inhomogeneous nonlinear Schrödinger equation ⋮ Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential ⋮ Classification of minimal mass blow-up solutions for an \({L^{2}}\) critical inhomogeneous NLS ⋮ Blowup and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schrödinger equation ⋮ Orbital stability via the energy-momentum method: the case of higher dimensional symmetry groups ⋮ Bifurcation from infinity for an asymptotically linear problem on the half-line ⋮ Orbital Stability: Analysis Meets Geometry
Cites Work
- Existence and orbital stability of standing waves for some nonlinear Schrödinger equations, perturbation of a model case
- On a class of nonlinear Schrödinger equations
- Guidance properties of nonlinear planar waveguides
- Nonlinear eigenvalue problems having an unbounded branch of symmetric bound states
- Uniqueness and stability of ground states for some nonlinear Schrödinger equations
- Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities
- Uniqueness of positive solutions of some semilinear Sturm–Liouville problems on the half line
- On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN
- Cases of equality and strict inequality in the extended Hardy–Littlewood inequalities
- Why are solitons stable?
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