scholarly journals A Higher Order Nonlinear Schrödinger Equation

2020 ◽  
Vol 4 (1) ◽  
pp. 28
Author(s):  
Edi Cahyono ◽  
Muh Zamrun Firihu ◽  
I Nyoman Sudiana ◽  
Herdi Budiman ◽  
Muh Kabil Djafar
Keyword(s):  
Wave Packet ◽  
Schrodinger Equation ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Media ◽  
Nonlinear Schrödinger ◽  
Complex Wave ◽  
Tremendous Amount ◽  
Fifth Order

Nonlinear Schrödinger (NLS) equation has been widely studied, and it has been appeared in tremendous amount of papers. NLS equation models a wave packet travelling in dispersive and nonlinear media. In this paper, a higher order NLS equation is discussed. The solution, which is complex wave envelope, is investigated numerically for narrow and broad envelope. Broader envelope shows deformation during the evolution, while narrow envelope does not. Another finding is that the fifth order nonlinearity does not contribute significantly to the envelope deformation. Hence, working with higher order will take much effort but insignificant results.

Higher-Order Rogue Waves for a Fifth-Order Dispersive Nonlinear Schrödinger Equation in an Optical Fibre

2015 ◽  
Vol 70 (5) ◽  
pp. 365-374 ◽  
Author(s):  
Qi-Min Wang ◽  
Yi-Tian Gao ◽  
Chuan-Qi Su ◽  
Yu-Jia Shen ◽  
Yu-Jie Feng ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
First Order ◽  
Nonlinear Schrödinger ◽  
Fifth Order

AbstractIn this article, a fifth-order dispersive nonlinear Schrödinger equation is investigated, which describes the propagation of ultrashort optical pulses, up to the attosecond duration, in an optical fibre. Rogue wave solutions are derived by virtue of the generalised Darboux transformation. Rogue wave structures and interaction are discussed through (i) the analyses on the higher-order rogue waves, the cubic, quartic, quintic, group-velocity, and phase-parameter effects; (ii) a higher-order rogue wave consisting of the first-order rogue waves via the interaction; (iii) characteristics of the rogue waves which are summarised, including the maximum/minimum values of the rogue waves and the number of the first-order rogue waves for composing the higher-order rogue wave; and (iv) spatial-temporal patterns which are illustrated and compared with those of the ‘self-focusing’ nonlinear Schrödinger equation. We find that the quintic terms increase the time of appearance for the first-order rogue waves which form the higher-order rogue wave, and that the quintic terms affect the interaction among the first-order rogue waves, which elongates the distance of appearance for the higher-order rogue wave.

New Rational Homoclinic Solution and Rogue Wave Solution for the Coupled Nonlinear Schrödinger Equation

2014 ◽  
Vol 69 (8-9) ◽  
pp. 441-445 ◽  
Author(s):  
Long-Xing Li ◽  
Jun Liu ◽  
Zheng-De Dai ◽  
Ren-Lang Liu
Keyword(s):  
Schrödinger Equation ◽  
Wave Solution ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Homoclinic Solution ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Rogue Wave Solution

In this work, the rational homoclinic solution (rogue wave solution) can be obtained via the classical homoclinic solution for the nonlinear Schrödinger (NLS) equation and the coupled nonlinear Schrödinger (CNLS) equation, respectively. This is a new way for generating rogue wave comparing with direct constructing method and Darboux dressing technique

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