2022/09/06 by Masashi Aiki, Aiki, Masashi
Physics and Astronomy · #35B35 #35Q35 #35Q55 #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2209.02224
openalex publication_date 2022/09/06 · openalex created_date 2022/09/08 · openalex updated_date 2026/07/28
We consider two nonlinear equations, the Localized Induction Equation and the cubic nonlinear Schrödinger Equation, and prove that the solvability of certain initial-boundary value problems for each equation is equivalent through the generalized Hasimoto transformation. As an application, we prove the orbital stability of plane wave solutions of the nonlinear Schrödinger equation based on stability estimates obtained for the Localized Induction Equation by the author in a paper in preparation. As far as the author knows, this is the first time that the analysis of the Localized Induction Equation, along with the Hasimoto transformation, provided new insight for the nonlinear Schrödinger equation.