Waveguide solutions for a nonlinear Schrödinger equation with mixed dispersion

DOI10.1007/978-3-319-19902-3_4zbMath1334.35310OpenAlexW2396338340MaRDI QIDQ5743913

Robson Nascimento, Denis Bonheure

Publication date: 9 February 2016

Published in: Contributions to Nonlinear Elliptic Equations and Systems (Search for Journal in Brave)

Full work available at URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/263702/4/F978-3-319-19902-3_4.pdf

zbMATH Keywords

Schrödinger equationground state solutionsbiharmonic NLSmixed dispersion NLSwaveguide solutions

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Antennas, waveguides in optics and electromagnetic theory (78A50) Lasers, masers, optical bistability, nonlinear optics (78A60) Semilinear elliptic equations (35J61)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sobolev spaces of symmetric functions and applications
• Nonlinear Schrödinger equations and sharp interpolation estimates
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Remarks on NLS with higher order anisotropic dispersion
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Symmetry properties in systems of semilinear elliptic equations
• Symétrie et compacité dans les espaces de Sobolev
• Existence of solitary waves in higher dimensions
• Introduction à la théorie des points critiques et applications aux problèmes elliptiques
• Symmetry results for semilinear elliptic systems in the whole space
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• Hamiltonian elliptic systems: a guide to variational frameworks
• Best constant for the embedding of the space \(H^ 2\cap H^ 1_ 0(\Omega)\) into \(L^{2N/(N-4)}\Omega\)
• Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
• Self-Focusing with Fourth-Order Dispersion
• Spectra of Linearized Operators for NLS Solitary Waves
• Uniqueness of positive radial solutions of semilinear elliptic equations in R^Nand séré's non—degeneracy condition
• Decay, symmetry and existence of solutions of semilinear elliptic systems
• Dispersion estimates for fourth order Schrödinger equations
• Blowup for Biharmonic NLS
• EXPONENTIAL DECAY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS
• Ground state and non-ground state solutions of some strongly coupled elliptic systems

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