scholarly journals Integrable nonlocal Hirota equations

2019 ◽  
Vol 60 (8) ◽  
pp. 081508 ◽  
Author(s):  
Julia Cen ◽  
Francisco Correa ◽  
Andreas Fring
Keyword(s):  
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 Dispersionless Hirota Equations and the Genus 3 Hyperelliptic Divisor

2019 ◽  
Vol 376 (2) ◽  
pp. 1397-1412
Author(s):  
Fabien Cléry ◽  
Evgeny V. Ferapontov
Keyword(s):  
Hirota Equations

Localised Nonlinear Waves in the Three-Component Coupled Hirota Equations

2017 ◽  
Vol 72 (11) ◽  
pp. 1053-1070 ◽  
Author(s):  
Tao Xu ◽  
Yong Chen
Keyword(s):  
Darboux Transformation ◽  
Dark Soliton ◽  
Lax Pair ◽  
Higher Order ◽  
Bright Soliton ◽  
Order Effects ◽  
Vector Solution ◽  
Hybrid Solutions ◽  
Three Components ◽  
Hirota Equations

AbstractWe construct the Lax pair and Darboux transformation for the three-component coupled Hirota equations including higher-order effects such as third-order dispersion, self-steepening, and stimulated Raman scattering. A special vector solution of the Lax pair with 4×4 matrices for the three-component Hirota system is elaborately generated, based on this vector solution, various types of mixed higher-order localised waves are derived through the generalised Darboux transformation. Instead of considering various arrangements of the three potential functions q1, q2, and q3, here, the same combination is considered as the same type solution. The first- and second-order localised waves are mainly discussed in six mixed types: (1) the hybrid solutions degenerate to the rational ones and three components are all rogue waves; (2) two components are hybrid solutions between rogue wave (RW) and breather (RW+breather), and one component is interactional solution between RW and dark soliton (RW+dark soliton); (3) two components are RW+dark soliton, and one component is RW+bright soliton; (4) two components are RW+breather, and one component is RW+bright soliton; (5) two components are RW+dark soliton, and one component is RW+bright soliton; (6) three components are all RW+breather. Moreover, these nonlinear localised waves merge with each other by increasing the absolute values of two free parameters α, β. These results further uncover some striking dynamic structures in the multicomponent coupled system.

On the bright and singular optical solitons to the ( $$2+1$$ 2 + 1 )-dimensional NLS and the Hirota equations

2018 ◽  
Vol 50 (3) ◽  
Author(s):  
Hasan Bulut ◽  
Tukur Abdulkadir Sulaiman ◽  
Haci Mehmet Baskonus ◽  
Tolga Aktürk
Keyword(s):  
Optical Solitons ◽  
Hirota Equations
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