A new class of Traveling Solitons for cubic Fractional Nonlinear Schrodinger equations

2015/01/07 by Younghun Hong, Yannick Sire, Hong, Younghun +1 · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1501.01415

openalex publication_date 2015/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the one-dimensional cubic fractional nonlinear Schrödinger equation i∂_tu-(-Δ)^σu+|u|²u=0, where σ∈ (\frac12,1) and the operator (-Δ)^σ is the fractional Laplacian of symbol |ξ|^2σ. Despite of lack of any Galilean-type invariance, we construct a new class of traveling soliton solutions of the form u(t,x)=e^-it(|k|^2σ-ω^2σ)Q_ω,k(x-2tσ|k|^2σ-2k), k∈ℝ, ωgt;0 by a rather involved variational argument.

Citations

• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations

Cited by

• Solitary-wave solutions of the fractional nonlinear Schrödinger equation. II. A numerical study of the dynamics
• Asymptotic decay of solitary wave solutions of the fractional nonlinear Schrödinger equation

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