Local Structure of Singular Profiles for a Derivative Nonlinear Schrödinger Equation
نویسندگان
چکیده
منابع مشابه
Direct perturbation theory for solitons of the derivative nonlinear Schrödinger equation and the modified nonlinear Schrödinger equation.
A direct perturbation theory for solitons of the derivative nonlinear Schrödinger (DNLS) equation is developed based on a closure of eigenfunctions of the linearized DNLS equation around a one-soliton solution. The slow evolution of soliton parameters and the perturbation-induced radiation are obtained. Under the known simple gaugelike transformation, these results are transformed into those fo...
متن کاملExact Multisoliton Solutions of General Nonlinear Schrödinger Equation with Derivative
Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.
متن کاملSingular Solutions of the Biharmonic Nonlinear Schrödinger Equation
We consider singular solutions of the L 2-critical biharmonic nonlinear Schrödinger equation. We prove that the blowup rate is bounded by a quartic-root, the solution approaches a quasi–self-similar profile, and a finite amount of L 2-norm, which is no less than the critical power, concentrates into the singularity. We also prove the existence of a ground-state solution. We use asymptotic analy...
متن کاملLow Regularity Local Well-Posedness of the Derivative Nonlinear Schrödinger Equation with Periodic Initial Data
The Cauchy problem for the derivative nonlinear Schrödinger equation with periodic boundary condition is considered. Local well-posedness for data u0 in the space b H r (T), defined by the norms ‖u0‖ b Hs r (T) = ‖〈ξ〉 s b u0‖lr′ ξ , is shown in the parameter range s ≥ 1 2 , 2 > r > 4 3 . The proof is based on an adaptation of the gauge transform to the periodic setting and an appropriate varian...
متن کاملStability of Solitary Waves for a Generalized Derivative Nonlinear Schrödinger Equation
We consider a derivative nonlinear Schrödinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability/instability results that depend on the strength of the nonlinearity and, in some instances, their velocity. We illustrate these results with numerical simulations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Applied Dynamical Systems
سال: 2017
ISSN: 1536-0040
DOI: 10.1137/16m1060339