scholarly journals Some novel soliton solution, breather solution and Darboux transformation for a generalized coupled Toda soliton hierarchy

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Fajun Yu ◽  
Li Li ◽  
Shuo Feng
Keyword(s):  
Soliton Solution ◽  
Darboux Transformation ◽  
Breather Solution ◽  
Soliton Hierarchy

DETERMINANT REPRESENTATION OF N-TIMES DARBOUX TRANSFORMATION FOR THE DEFOCUSING NONLINEAR SCHRÖDINGER EQUATION

2013 ◽  
Vol 27 (29) ◽  
pp. 1350216 ◽  
Author(s):  
JINGWEI HAN ◽  
JING YU ◽  
JINGSONG HE
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Determinant Representation

The determinant expression T[N] of a new Darboux transformation (DT) for the Ablowitz–Kaup–Newell–Segur equation are given in this paper. By making use of this DT under the reduction r = q*, we construct determinant expressions of dark N-soliton solution for the defocusing NLS equation. Except known one-soliton, we provide smooth two-soliton and smooth N-soliton on a certain domain of parameter for the defocusing NLS equation.

The order-n breather and degenerate breather solutions of the (2+1)-dimensional cmKdV equations

2021 ◽  
Vol 35 (04) ◽  
pp. 2150053
Author(s):  
Feng Yuan
Keyword(s):  
Plane Wave ◽  
Darboux Transformation ◽  
Taylor Expansion ◽  
Degradation Process ◽  
Dynamic Evolution ◽  
Breather Solution ◽  
De Vries ◽  
Evolution With Time ◽  
Explicit Expressions

Starting with a plane wave seed, the order-[Formula: see text] breather for the (2+1)-D complex modified Korteweg-de Vries (cmKdV) equations is obtained by the use of Darboux transformation. The dynamic evolution of order-2 and order-3 breather solutions is shown in the form of pictures. Afterward, we obtain the order-[Formula: see text] degenerate breather solution by using the Taylor expansion concerning the limits [Formula: see text] and focus on the order-2 degenerate breather solution. We show the dynamic evolution with time and discuss the degradation process from a breather solution through getting [Formula: see text] closer and closer to [Formula: see text]. Furthermore, the approximate trajectories of the order-2, order-3, order-4 degenerate breather solutions are depicted by explicit expressions, respectively.

scholarly journals On the continuum limit for a semidiscrete Hirota equation

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160628 ◽  
Author(s):  
Andrew Pickering ◽  
Hai-qiong Zhao ◽  
Zuo-nong Zhu
Keyword(s):  
Soliton Solution ◽  
Darboux Transformation ◽  
Explicit Solution ◽  
Continuum Limit ◽  
Lax Pair ◽  
Discrete Space ◽  
Hirota Equation ◽  
Space Step ◽  
The Continuum

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 δ affects the simulation for the soliton solution to the Hirota equation. The Darboux transformation and explicit solution for the semidiscrete Hirota equation are constructed. We show that the continuum limit for the semidiscrete Hirota equation, including the Lax pair, the Darboux transformation and the explicit solution, yields the corresponding results for the Hirota equation as δ → 0 .

scholarly journals Darboux transformation and exact solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials

2016 ◽  
Vol 13 (01) ◽  
pp. 1550134 ◽  
Author(s):  
Z. S. Yersultanova ◽  
M. Zhassybayeva ◽  
K. Yesmakhanova ◽  
G. Nugmanova ◽  
R. Myrzakulov
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Integrable Systems ◽  
Self Consistent

Integrable Heisenberg ferromagnetic equations are an important subclass of integrable systems. The M-XCIX equation is one of a generalizations of the Heisenberg ferromagnetic equation and are integrable. In this paper, the Darboux transformation of the M-XCIX equation is constructed. Using the DT, a 1-soliton solution of the M-XCIX equation is presented.

DARBOUX TRANSFORMATION OF THE MODIFIED TODA LATTICE EQUATION

2006 ◽  
Vol 20 (11) ◽  
pp. 641-648 ◽  
Author(s):  
XI-XIANG XU ◽  
HONG-XIANG YANG ◽  
YE-PENG SUN
Keyword(s):  
Spectral Problem ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Toda Lattice ◽  
Lattice Equation ◽  
Matrix Spectral Problem ◽  
Toda Lattice Equation

A modified Toda lattice equation associated with a properly discrete matrix spectral problem is introduced. Darboux transformation for the resulting lattice equation is constructed. As an application, the soliton solution for the Toda lattice equation is explicitly given.

SOLITON PROPAGATION IN NONUNIFORM OPTICAL FIBERS

2003 ◽  
Vol 12 (03) ◽  
pp. 341-348 ◽  
Author(s):  
YAN XIAO ◽  
ZHIYONG XU ◽  
LU LI ◽  
ZHONGHAO LI ◽  
GUOSHENG ZHOU
Keyword(s):  
Optical Fibers ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Transmission System ◽  
Soliton Propagation ◽  
Soliton Transmission System ◽  
Soliton Transmission

In this paper, we construct the Lax pair for a soliton transmission system in nonuniform optical fibers and give N-soliton solution using the Darboux transformation. The explicit one-soliton and two-soliton solutions are presented. Further, we discuss the interaction scenario between two neighboring solitons and the effect of the inhomogeneities of the fiber (z0) on the interaction between two neighboring solitons.

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