Nonintegrable spatial discrete nonlocal nonlinear schrödinger equation.

Integrable and nonintegrable discrete nonlinear Schrödinger equations (NLS) are significant models to describe many phenomena in physics. Recently, Ablowitz and Musslimani introduced a class of reverse space, reverse time, and reverse space-time nonlocal integrable equations, including the nonlocal NLS equation, nonlocal sine-Gordon equation, nonlocal Davey-Stewartson equation, etc. Moreover, the integrable nonlocal discrete NLS has been exactly solved by inverse scattering transform.

A coupled focusing-defocusing complex short pulse equation: Multisoliton, breather, and rogue wave.

Nonlinear Schrödinger equation, short pulse equation, and complex short pulse equation have important applications in nonlinear optics. They can be derived from the Maxwell equations. In this paper, we investigate a coupled focusing-defocusing complex short pulse equation.

Reply to "Comment on 'Defocusing complex short-pulse equation and its multi-dark-soliton solution' ".

Our paper [Phys. Rev. E 93, 052227 (2016)PREHBM2470-004510.

On the continuum limit for a semidiscrete Hirota equation.

In this paper, we propose a new semidiscrete Hirota equation which yields the Hirota equation in the continuum limit. We focus on the topic of how the discrete space step affects the simulation for the soliton solution to the Hirota equation. The Darboux transformation and explicit solution for the semidiscrete Hirota equation are constructed.

Defocusing complex short-pulse equation and its multi-dark-soliton solution.

In this paper, we propose a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrödinger (NLS) equation in the ultrashort-pulse regime. Furthermore, we construct the multi-dark-soliton solution for the defocusing complex short-pulse equation through the Darboux transformation and reciprocal (hodograph) transformation.

Nonintegrable semidiscrete Hirota equation: gauge-equivalent structures and dynamical properties.

In this paper, we investigate nonintegrable semidiscrete Hirota equations, including the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation. We focus on the topics on gauge-equivalent structures and dynamical behaviors for the two nonintegrable semidiscrete equations. By using the concept of the prescribed discrete curvature, we show that, under the discrete gauge transformations, the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation are, respectively, gauge equivalent to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation.