Bilinearization of a Generalized Derivative Nonlinear Schrödinger Equation

Bilinearization of a Generalized Derivative Nonlinear Schrödinger Equation

A generalized derivative nonlinear Schrödinger equation, iqt + qxx + 2iγ|q| qx + 2i(γ − 1)q q x + (γ − 1)(γ − 2)|q| q = 0, is studied by means of Hirota’s bilinear formalism. Soliton solutions are constructed as quotients of Wronski-type determinants. A relationship between the bilinear structure and gauge transformation is also discussed. ∗e-mail: [email protected] §

Stability 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.

Exact 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.

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...

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation.