Nth-order smooth positon and breather-positon solutions for the generalized integrable discrete nonlinear Schrödinger equation

Breather solutions of the integrable quintic nonlinear Schrödinger equation and their interactions.

We present breather solutions of the quintic integrable equation of the Schrödinger hierarchy. This equation has terms describing fifth-order dispersion and matching nonlinear terms. Using a Darboux transformation, we derive first-order and second-order breather solutions. These include first- and second-order rogue-wave solutions. To some extent, these solutions are analogous with the correspo...

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation.

Second-order nonlinear Schrödinger equation breather solutions in the degenerate and rogue wave limits.

We present an explicit analytic form for the two-breather solution of the nonlinear Schrödinger equation with imaginary eigenvalues. It describes various nonlinear combinations of Akhmediev breathers and Kuznetsov-Ma solitons. The degenerate case, when the two eigenvalues coincide, is quite involved. The standard inverse scattering technique does not generally provide an answer to this scenario...

Breather and rogue wave solutions of a generalized nonlinear Schrödinger equation.

In this paper, using the Darboux transformation, we demonstrate the generation of first-order breather and higher-order rogue waves from a generalized nonlinear Schrödinger equation with several higher-order nonlinear effects representing femtosecond pulse propagation through nonlinear silica fiber. The same nonlinear evolution equation can also describe the soliton-type nonlinear excitations i...

Nonsingular Positon and Complexiton Solutions for the Coupled Kdv System

Taking the coupled KdV system as a simple example, analytical and nonsingular complexiton solutions are firstly discovered in this letter for integrable systems. Additionally, the analytical and nonsingular positon-negaton interaction solutions are also firstly found for S-integrable model. The new analytical positon, negaton and complexiton solutions of the coupled KdV system are given out bot...