N-fold binary Darboux transformation for the nth-order Ablowitz-Kaup-Newell-Segur system under a pseudo-symmetry hypothesis

2021 ◽  
pp. 107719
Author(s):  
Jing-Jing Su ◽  
Bo Ruan
Keyword(s):  
Darboux Transformation ◽  
Symmetry Hypothesis ◽  
Binary Darboux Transformation

Determinant Representation of Binary Darboux Transformation for the AKNS Equation

2015 ◽  
Vol 70 (12) ◽  
pp. 1039-1048 ◽  
Author(s):  
Jing Yu ◽  
Jingwei Han ◽  
Jingsong He
Keyword(s):  
Darboux Transformation ◽  
Darboux Transformations ◽  
Nls Equation ◽  
Reduction Condition ◽  
Nonlinear Schrödinger ◽  
Determinant Representation ◽  
Akns Equation ◽  
New Form ◽  
Binary Darboux Transformation

AbstractIn this paper, the determinant representation of the n-fold binary Darboux transformation, which is a 2×2 matrix, for the Ablowitz–Kaup–Newell–Segur equation is constructed. In this 2×2 matrix, each element is expressed by (2n+1)-order determinants. When the reduction condition r=–q̅ is considered, we obtain one of binary Darboux transformations for the nonlinear Schrödinger (NLS) equation. As its applications, several solutions are constructed for the NLS equation. Especially, a new form of two-soliton is given explicitly.

Bound-state solitons for a non-linear Schrödinger system with the negatively coherent coupling in a weakly birefringent fiber

2020 ◽  
Vol 34 (36) ◽  
pp. 2050423
Author(s):  
Jie Zhang ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
Chen-Rong Zhang ◽  
Xia-Xia Du ◽  
...  
Keyword(s):  
Darboux Transformation ◽  
Bound State ◽  
Optical Pulses ◽  
Coherent Coupling ◽  
Non Linear ◽  
Optical Modes ◽  
Binary Darboux Transformation ◽  
Birefringent Fiber ◽  
Schrödinger System

In this paper, we study a non-linear Schrödinger system with the negatively coherent coupling in a weakly birefringent fiber for two orthogonally polarized optical pulses. With respect to the slowly-varying envelopes of two interacting optical modes and based on the existing binary Darboux transformation, we obtain four types of the bound-state solitons: degenerate-I, degenerate-II, degenerate–non-degenerate, and non-degenerate–non-degenerate bound-state solitons. We graphically analyze the interactions between the degenerate or non-degenerate solitons and four types of the bound-state solitons. When the degenerate solitons interact with the bound-state solitons, amplitudes and widths of the degenerate solitons remain unchanged. When the non-degenerate solitons interact with the bound-state solitons, amplitudes and widths of the bound-state solitons remain unchanged.

Quasi-Grammian solutions of the generalized Heisenberg magnet model

2020 ◽  
Vol 98 (3) ◽  
pp. 303-311
Author(s):  
Z. Amjad ◽  
B. Haider
Keyword(s):  
Darboux Transformation ◽  
Lie Group ◽  
Soliton Solutions ◽  
Two Dimensions ◽  
Explicit Solutions ◽  
Heisenberg Magnet ◽  
Model Based ◽  
Binary Darboux Transformation

In this paper we use standard binary Darboux transformation to obtain the quasi-Grammian multi-soliton solutions of generalized Heisenberg magnet model in two dimensions. We also discuss the model based on the Lie group SU(n) and obtain explicit solutions of the model for the SU(2) case.

A binary Darboux transformation for the Toda lattice

1986 ◽  
Vol 35 (4) ◽  
pp. 2582-2589 ◽  
Author(s):  
V. M. Babich ◽  
V. B. Matveev ◽  
M. A. Sail'
Keyword(s):  
Darboux Transformation ◽  
Toda Lattice ◽  
Binary Darboux Transformation
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