Related papers: A focusing and defocusing semi-discrete complex sh…
In this article, a fully discrete short pulse (SP) equation is presented as an integrability condition of a linear system of difference equations (also known as discrete Lax pair). Additionally, two semi-discrete versions of the SP equation…
In this paper, we propose a complex short pulse equation of both focusing and defocusing types, which governs the propagation of ultra-short pulses in nonlinear optical fibers. It can be viewed as an analogue of the nonlinear Schr\"odinger…
In the present paper, we study the defocusing complex short pulse (CSP) equations both geometrically and algebraically. From the geometric point of view, we establish a link of the complex coupled dispersionless (CCD) system with the motion…
The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact solutions including bright soliton, dark-soliton, breather…
In the present paper, we are concerned with the general localized solutions for the complex short pulse equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the…
In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key of the construction is the bilinear forms and determinant structure of solutions of the CSP…
We address the long-time asymptotics of the solution to the Cauchy problem of ccSP (coupled complex short pulse) equation on the line for decaying initial data that can support solitons. The ccSP system describes ultra-short pulse…
In the present paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key of the construction is the bilinear forms and determinant structure of solutions of the SP equation. We also…
In this paper, we primarily construct Darboux transformation(DT) of the nonlocal coupled modified complex integrable dispersionless (cm-CID) equation, which is first proposed by the connection with a nonlocal coupled modified complex short…
Nonlinear Schr\"odinger equation, short pulse equation and complex short pulse equation have important application in nonlinear optics. They can be derived from the Maxwell equation. In this paper, we investigate a coupled…
We derive two new solutions in terms of elliptic functions, one for the dark and one for the bright soliton regime, for the semi-discrete cubic nonlinear Schroedinger equation of Ablowitz and Ladik. When considered in the complex plane,…
This manuscript explores the Darboux transformation employed in the construction of exactly solvable models for pseudospin-one particles described by the Dirac-type equation. We focus on the settings where a flat band of zero energy is…
We employ the $\bar{\partial}$-steepest descent method in order to investigate the Cauchy problem of the complex short pulse (CSP) equation with initial conditions in weighted Sobolev space $H^{1,1}(\mathbb{R})=\{f\in L^{2}(\mathbb{R}):…
The focus of this work is on a class of solutions of the defocusing Ablowitz-Ladik lattice on an arbitrarily large background which are discrete analogs of the Kuznetsov-Ma (KM) breathers of the focusing nonlinear Schrodinger equation. One…
The short pulse (SP) equation is a novel model equation describing the propagation of ultra-short optical pulses in nonlinear media. This article reviews some recent results about the SP equation. In particular, we focus our attention on…
An integrable semi-discretization of complex and multi-component coupled dispersionless systems via Lax pairs is presented. A Lax pair is proposed for the complex sdCD system. We derive the Lax pair for the multi-component sdCD system…
The purpose of the present paper is to develop the inverse scattering transform for the nonlocal semi-discrete nonlinear Schrodinger equation (known as Ablowitz-Ladik equation) with PT-symmetry. This includes: the eigenfunctions (Jost…
In this paper, we study the Cauchy problem and multi-soliton solutions for a two-component short pulse system. For the Cauchy problem, we first prove the existence and uniqueness of solution with an estimate of the analytic lifespan, and…
The Sasa-Satsuma equation, a higher-order nonlinear Schr\"{o}dinger equation, is an important integrable equation, which displays the propagation of femtosecond pulses in optical fibers. In this paper, we investigate a generalized…
We propose a novel multi-component system of nonlinear equations that generalizes the short pulse (SP) equation describing the propagation of ultra-short pulses in optical fibers. By means of the bilinear formalism combined with a hodograph…