Projects per year
Abstract
We study the stability theory of solitary wave solutions for the generalized derivative nonlinear Schrödinger equation i∂_{t}u + ∂_{x}^{2}u + iu^{2σ}∂_{x}u = 0. The equation has a twoparameter family of solitary wave solutions of the form ϕ_{ω,c}(x) = φ_{ω,c}(x) exp { i _{2}^{c} x − _{2σ}^{i}_{+ 2}^{Z}_{−∞}^{x} φ^{2}_{ω,c}^{σ} (y)dy }. Here φ_{ω,c} is some realvalued function. It was proved in [29] that the solitary wave solutions are stable if −2√ω < c < 2z_{0}^{√}ω, and unstable if 2z_{0}^{√}ω < c < 2√ω for some z_{0} ∈ (0, 1). We prove the instability at the borderline case c = 2z_{0}^{√}ω for 1 < σ < 2, improving the previous results in [7] where 7/6 < σ < 2.
Original language  English 

Pages (fromto)  339375 
Number of pages  37 
Journal  Mathematical Research Letters 
Volume  27 
Issue number  2 
DOIs  
Publication status  Published  2020 
Projects
 1 Finished

Harmonic analysis and dispersive partial differential equations
Guo, Z., Li, J., Kenig, C. & Nakanishi, K.
Australian Research Council (ARC), Monash University, Macquarie University, University of Chicago, Osaka University
1/01/17 → 1/11/20
Project: Research