Soliton solutions for fractional Schrödinger equations

DOI10.1016/j.aml.2015.10.006zbMath1330.35504OpenAlexW1831648717MaRDI QIDQ899409

Xian Wu, Quanqing Li

Publication date: 28 December 2015

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2015.10.006

zbMATH Keywords

soliton solutionfractional Schrödinger equationminimization argument

Mathematics Subject Classification ID

Soliton solutions (35C08) Fractional partial differential equations (35R11)

Related Items (12)

Finite difference schemes for time-fractional Schrödinger equations via fractional linear multistep method ⋮ Soliton dynamics in a fractional complex Ginzburg-Landau model ⋮ Existence of nontrivial solutions for fractional Schrödinger equations with electromagnetic fields and critical or supercritical nonlinearity ⋮ Weak solutions for the stationary Schrödinger equation and its application ⋮ Ground states for fractional Schrödinger equations with electromagnetic fields and critical growth ⋮ Propagation of three-dimensional optical solitons in fractional complex Ginzburg-Landau model ⋮ Nontrivial solutions for fractional Schrödinger equations with electromagnetic fields and critical or supercritical growth ⋮ Continuity of weak solutions to an elliptic problem on p$$ p $$‐fractional Laplacian ⋮ An existence result for a generalized quasilinear Schrödinger equation with nonlocal term ⋮ A stable numerical method for multidimensional time fractional Schrödinger equations ⋮ Orbital stability of standing waves for nonlinear fractional Schrödinger equation with unbounded potential ⋮ Ground state solutions for fractional Schrödinger equations with critical exponents

Cites Work

• Existence of entire solutions for a class of quasilinear elliptic equations
• Hitchhiker's guide to the fractional Sobolev spaces
• Elliptic problems involving the fractional Laplacian in \(\mathbb R^N\)
• A critical Kirchhoff type problem involving a nonlocal operator
• Sign-changing critical points from linking type theorems
• Soliton solutions for quasilinear Schrödinger equations, I
• Ground states for fractional Schrödinger equations with critical growth

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