Regularity of ground state solutions of dispersion managed nonlinear Schrödinger equations

DOI10.1016/j.jde.2004.10.006zbMath1072.35172OpenAlexW1975489238MaRDI QIDQ1763956

Xianqiang Yang

Publication date: 22 February 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2004.10.006

zbMATH Keywords

regularityground statesdispersion managed nonlinear Schrödinger equation

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (12)

Decay estimates and smoothness for solutions of the dispersion managed non-linear Schrödinger equation ⋮ Exponential decay of dispersion-managed solitons for general dispersion profiles ⋮ Diffraction managed solitons with zero mean diffraction ⋮ Continuum limit related to dispersion managed nonlinear Schrödinger equations ⋮ Well-posedness of dispersion managed nonlinear Schrödinger equations ⋮ Unnamed Item ⋮ Uniqueness of a Minimizer for a Variational Problem Related to the Dispersion Managed Nonlinear Schrödinger Equation ⋮ On non-local variational problems with lack of compactness related to non-linear optics ⋮ Super-exponential decay of diffraction managed solitons ⋮ Thresholds for Existence of Dispersion Management Solitons for General Nonlinearities ⋮ Stability of dispersion managed solitons for vanishing average dispersion ⋮ Maximisers for Strichartz inequalities on the torus

Cites Work

• On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• On the existence of a maximizer for the Strichartz inequality
• The singular perturbation limit of a variational problem from nonlinear fiber optics
• Maximizers for the Strichartz inequality
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• Infinitely many radial solutions of a variational problem related to dispersion-managed optical fibers
• Stabilizing effects of dispersion management

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