Degenerate solutions for the spatial discrete Hirota equation

2020 ◽  
Vol 102 (3) ◽  
pp. 1825-1836
Author(s):  
Meng Li ◽  
Maohua Li ◽  
Jingsong He
Keyword(s):  
Hirota Equation ◽  
Degenerate Solutions

scholarly journals New optical solitons of perturbed nonlinear Schrödinger-Hirota equation with spatio-temporal dispersion

2021 ◽  
pp. 104656
Author(s):  
Lanre Akinyemi ◽  
Hadi Rezazadeh ◽  
Qiu-Hong Shi ◽  
Mustafa Inc ◽  
Mostafa M.A. Khater ◽  
...  
Keyword(s):  
Optical Solitons ◽  
Hirota Equation ◽  
Nonlinear Schrödinger ◽  
Spatio Temporal ◽  
Temporal Dispersion

Inelastic Interaction of Double-Valley Dark Solitons for the Hirota Equation

2021 ◽  
Vol 38 (9) ◽  
pp. 090201
Author(s):  
Xiao-Man Zhang ◽  
Yan-Hong Qin ◽  
Li-Ming Ling ◽  
Li-Chen Zhao
Keyword(s):  
Inelastic Interaction ◽  
Hirota Equation ◽  
Dark Solitons

A Criterion for Decomposabilty in QYBE

2021 ◽  
Author(s):  
Sergio Camp-Mora ◽  
Raúl Sastriques
Keyword(s):  
Structure Group ◽  
Trivial Case ◽  
Degenerate Solutions

Abstract In this paper, set theoretic solutions of the Quantum Yang–Baxter Equations are considered. Etingof et al. [ 8] defined the structure group for non-degenerate solutions and gave some properties of this group. In particular, they provided a criterion for decomposability of involutive solutions based on the transitivity of the structure group. In that paper, the diagonal permutation $T$ is also introduced. It is known that this permutation is trivial exactly when the solution is square free. Rump [ 12] proved that these solutions are decomposable except in the trivial case. Later, Ramirez and Vendramin [ 11] gave some criteria for decomposability related with the diagonal permutation $T$. In this paper it was proven that an involutive solution is decomposable when the number of symbols of the solution and the order of the diagonal permutation $T$ are coprime.

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