Existence of the stable traveling wave for half-wave equation with L2-critical combined nonlinearities. Issue 7 (3rd May 2022)

• Record Type: Journal Article
• Authors: Li, Yuan; Zhao, Dun; Wang, Qingxuan
• Is Part Of: Applicable analysis. Volume 101:Issue 7(2022)
• Page Start: 2498
• Page End: 2510
• Publication Date: 2022-05-03
• Subjects: Half-wave equation -- L2-mass critical nonlinearity -- traveling wave -- concentration compactness -- orbital stability; 35Q41 -- 35Q55 -- 35J20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1811976
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : For the Cauchy problem of the half-wave equation with L 2 -critical combined nonlinearities 1 i ψ t = − Δ ψ − | ψ | 2 / N ψ − | ψ | p ψ, 0 < p < 2 N ( N ≥ 2 ), ψ ( 0, x ) = ψ 0 ( x ), we obtain the existence of traveling wave solution of the form ψ ( t, x ) = e i t μ u v ( x − v t ) with 0 < | v | < 1 . If ∥ ψ 0 ∥ 2 < ∥ Q v ∥ 2, where Q v is a solution of the equation 2 − Δ u v + i ( v ⋅ ∇ ) u v − | u v | 2 / N u v = − u v, we prove that the traveling wave is stable.