Related papers: Darboux transformation and solitonic solution to t…
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…
In this paper, we construct a generalized Darboux transformation to the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and inelastic Raman scattering terms. As application, an Nth-order…
Using the Darboux transformation for the Korteweg-de Vries equation, we construct and analyze exact solutions describing the interaction of a solitary wave and a traveling cnoidal wave. Due to their unsteady, wavepacket-like character,…
The Darboux Dressing Transformations developed in our previous paper (Multicomponent integrable wave equations I. Darboux-Dressing Transformation, J. Phys. A: Math. Theor. 40, 961-977, 2007) are here applied to construct soliton solutions…
We study a discrete Darboux transformation and construct the multi-soliton solutions in terms of ratio of determinants for integrable discrete sine-Gordon equation. We also calculate explicit expressions of single, double, triple, quad…
We present a unified operator-theoretic framework for constructing deterministic KdV soliton gases and step-type KdV solutions. Starting from Dyson's determinantal formula, we obtain a broad class of reflectionless solutions and describe…
In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch(H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fibre and further generalize it to the matrix form of the $n$-fold…
The Darboux transformation (DT) formulae for the derivative nonlinear Schr\"{o}dinger (DNLS) equation are expressed in concise forms, from which the multi-solitons, n-periodic solutions, higher-order hybrid-pattern solitons and some mixed…
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…
This paper delves into the study of multi-component derivative nonlinear Schrodinger (n-DNLS) equations featuring nonzero boundary conditions. Employing the Darboux transformation (DT) method, we derive higher-order vector rogue wave…
Rarefactive waves and dispersive shock waves are generated from the step-like initial data in many nonlinear evolution equations including the classical example of the Korteweg-de Vries (KdV) equation. When a solitary wave is injected on…
A one-fold Darboux transformation between solutions of the semi-discrete massive Thirring model is derived using the Lax pair and dressing methods. This transformation is used to find the exact expressions for soliton solutions on zero and…
In this work, we study the dynamics of rogue waves in the partially $\cal{PT}$-symmetric nonlocal Davey-Stewartson(DS) systems. Using the Darboux transformation method, general rogue waves in the partially $\cal{PT}$-symmetric nonlocal DS…
The discrete Schr\"odinger equation on a half-line lattice with the Dirichlet boundary condition is considered when the potential is real valued, is summable, and has a finite first moment. The Darboux transformation formulas are derived…
An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schr\"{o}dinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the…
This work focuses on three-component defocusing Kundu-Eckhaus equation, which serves as a significant coupled model for describing complex wave propagation in nonlinear optical fibers. By employing binary Darboux transformation based on 4x4…
In this paper, we obtain a uniform Darboux transformation for multi-component coupled NLS equations, which can be reduced to all previous presented Darboux transformation. As a direct application, we derive the single dark soliton and…
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…
In this work, inverse scattering transform for the sixth-order nonlinear Schr\"{o}dinger equation with both zero and nonzero boundary conditions at infinity is given, respectively. For the case of zero nonzero boundary conditions, in terms…
In this paper, the generalized Darboux transformation is established to the AB system, which mainly describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. We find a unified…