Instability of the solitary wave solutions for the genenalized derivative Nonlinear Schrödinger equation in the critical frequency case

2018/03/21 by Zihua Guo, Guo, Zihua, Cui Ning +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1803.07700

Abstract

We study the stability theory of solitary wave solutions for the generalized derivative nonlinear Schrödinger equation i∂_tu+∂_x²u+i|u|^2σ∂_x u=0. The equation has a two-parameter family of solitary wave solutions of the form ϕ_ω,c(x)=φ_ω,c(x)exp\ i\frac c2 x-(i)/(2σ+2)∫_-∞^xφ^2σ_ω,c(y)dy\. Here φ_ω,c is some real-valued function. It was proved in \citeLiSiSu1 that the solitary wave solutions are stable if -2√(ω)

Citations

• On the modulational instability of hydromagnetic waves parallel to the magnetic field

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