Infinitely many radial solutions of a variational problem related to dispersion-managed optical fibers

DOI10.1090/S0002-9939-02-06780-1zbMath1031.35135OpenAlexW1568225275MaRDI QIDQ4804068

Markus Kunze

Publication date: 10 April 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06780-1

zbMATH Keywords

symmetrycritical pointscompactnessnonlinear opticsbound statesnonlocal variational problemdispersion-managed solitons

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (6)

Diffraction managed solitons with zero mean diffraction ⋮ Unnamed Item ⋮ Blow-up profile to solutions of NLS with oscillating nonlinearities ⋮ Stabilizing blow up solutions to nonlinear Schrödinger equations ⋮ Regularity of ground state solutions of dispersion managed nonlinear Schrödinger equations ⋮ Blow-up solutions to the nonlinear Schrödinger equation with oscillating nonlinearities

Cites Work

• Unnamed Item
• The principle of symmetric criticality
• Nonlinear scalar field equations. I: Existence of a ground state
• Existence of solitary waves in higher dimensions
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Dispersion-managed solitons via an averaged variational principle
• Minimax theorems
• The dispersion-managed soliton as a ground state of a macroscopic nonlinear quantum oscillator
• Bifurcation from the essential spectrum without sign condition on the nonlinearity
• Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions
• Stabilizing effects of dispersion management

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