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math.AP2026
Orbital Stability of Solitons and Scattering Theory for the Perturbed Derivative Nonlinear Schrödinger Equation
Phan Van Tin
We consider the following derivative nonlinear Schrödinger equation with a single power-type perturbation \begin{equation*} i\partial_tu+\partial_x^2u+i|u|^2\partial_xu+b |u|^pu=0,…
math.AP2022
Instability of Multi-Solitons for Derivative Nonlinear Schr{ö}dinger Equations
Phan van Tin
In [19] and [26], the authors proved the stability of multi-solitons for derivative nonlinear Schr{ö}dinger equations. Roughly speaking, sum of finite stable solitons is stable. We…
math.AP2021★ 1 cited
On The Cauchy Problem For A Derivative Nonlinear Schr{ö}Dinger Equation With Nonvanishing Boundary Conditions
Phan van Tin
In this paper we consider the Schr{ö}dinger equation with nonlinear derivative term. Our goal is to initiate the study of this equation with non vanishing boundary conditions. We o…