The ∂̄-dressing method and soliton solutions for the three-component coupled Hirota equations

2021 ◽  
Vol 62 (9) ◽  
pp. 093510
Author(s):  
Zi-Yi Wang ◽  
Shou-Fu Tian ◽  
Jia Cheng
Keyword(s):  
Soliton Solutions ◽  
Dressing Method ◽  
Hirota Equations

scholarly journals ON THE APPLICATION OF A GENERALIZED VERSION OF THE DRESSING METHOD TO THE INTEGRATION OF VARIABLE COEFFICIENT N-COUPLED NONLINEAR SCHRÖDINGER EQUATION

2012 ◽  
Vol 19 (04) ◽  
pp. 1250028
Author(s):  
TING SU ◽  
HUIHUI DAI ◽  
XIAN GUO GENG
Keyword(s):  
Optical Fibers ◽  
Variable Coefficient ◽  
High Order ◽  
Explicit Solutions ◽  
Compatibility Conditions ◽  
Dressing Method ◽  
Integrable Equations ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Hirota Equations

N-coupled nonlinear Schrödinger (NLS) equations have been proposed to describe N-pulse simultaneous propagation in optical fibers. When the fiber is nonuniform, N-coupled variable-coefficient NLS equations can arise. In this paper, a family of N-coupled integrable variable-coefficient NLS equations are studied by using a generalized version of the dressing method. We first extend the dressing method to the versions with (N + 1) × (N + 1) operators and (2N + 1) × (2N + 1) operators. Then, we obtain three types of N-coupled variable-coefficient equations (N-coupled NLS equations, N-coupled Hirota equations and N-coupled high-order NLS equations). Then, the compatibility conditions are given, which insure that these equations are integrable. Finally, the explicit solutions of the new integrable equations are obtained.

scholarly journals Noncommutative Multisoliton Solutions of a Supersymmetric Chiral Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Xiujuan Zhu
Keyword(s):  
Soliton Solutions ◽  
Chiral Model ◽  
Property A ◽  
Dressing Method ◽  
Multisoliton Solutions

Multisoliton configurations of a superextended and Moyal-type noncommutative deformed modified2+1chiral model have been constructed with the dressing method by Lechtenfeld and Popov several years ago. These configurations have no-scattering property. A two-soliton configuration with nontrivial scattering was constructed soon after that. More multisoliton solutions with general pole data of the superextended and noncommutative Ward model will be constructed in this paper. The method is the supersymmetric and noncommutative extension of Dai and Terng’s in constructing soliton solutions of the Ward model.

ON THE DRESSING METHOD FOR THE GENERALIZED COUPLED DISPERSIONLESS INTEGRABLE SYSTEM

2013 ◽  
Vol 28 (20) ◽  
pp. 1350088 ◽  
Author(s):  
NOSHEEN MUSHAHID ◽  
MAHMOOD UL HASSAN
Keyword(s):  
Integrable System ◽  
Lie Group ◽  
Matrix Equation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Two Dimensions ◽  
Nonlinear Matrix Equation ◽  
Dressing Method ◽  
Nonlinear Matrix ◽  
Funct Anal

The dressing method of Zakharov and Shabat [Funct. Anal. Appl.8, 226 (1974) and ibid.13, 166 (1980)] has been employed to the generalized coupled dispersionless integrable system in two dimensions. The dressed solutions to the Lax pair and to the nonlinear matrix equation have been obtained in terms of Hermitian projectors. The dressing method has been related with the quasi-determinant solutions obtained by using the standard matrix Darboux transformation. The iteration of dressing procedure has been shown to give N-soliton solutions of the system. At the end, the explicit soliton solution has been obtained for the system based on Lie group SU(2).

scholarly journals ABELIAN TODA SOLITONS REVISITED

2008 ◽  
Vol 20 (10) ◽  
pp. 1209-1248 ◽  
Author(s):  
KH. S. NIROV ◽  
A. V. RAZUMOV
Keyword(s):  
Soliton Solutions ◽  
General Linear ◽  
Linear Groups ◽  
Loop Groups ◽  
Dressing Method ◽  
Detailed Review ◽  
Hirota’S Method ◽  
General Linear Groups ◽  
Toda Systems ◽  
Hirota's Method

We present a systematic and detailed review of the application of the method of Hirota and the rational dressing method to abelian Toda systems associated with the untwisted loop groups of complex general linear groups. Emphasizing the rational dressing method, we compare the soliton solutions constructed within these two approaches, and show that the solutions obtained by the Hirota's method are a subset of those obtained by the rational dressing method.

scholarly journals Explicit Solutions of Integrable Variable-coeffcient Cylindrical Toda Equations

2020 ◽  
pp. 1-9
Author(s):  
Ting Su ◽  
Jia Wang ◽  
Quan Zhen Huang
Keyword(s):  
Soliton Solution ◽  
Compatibility Condition ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Explicit Solutions ◽  
Dressing Method ◽  
New Type ◽  
Toda Equations ◽  
Toda Lattice Equations

Integrable cylindrical Toda lattice equations are proposed by utilizing a generalized version of the dressing method. A compatibility condition is given which insures that these equations are integrable. Further, soliton solutions for new type equations are shown in explicit forms, including one soliton solution and two soliton solutions, respectively.

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