scholarly journals Impact of fifth order dispersion on soliton solution for higher order NLS equation with variable coefficients

2020 ◽  
Vol 5 (3) ◽  
pp. 205-213
Author(s):  
Angelin Vithya ◽  
M.S. Mani Rajan
Keyword(s):  
Soliton Solution ◽  
Variable Coefficients ◽  
Higher Order ◽  
Nls Equation ◽  
Fifth Order ◽  
Order Dispersion

scholarly journals Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 57
Author(s):  
Max-Olivier Hongler
Keyword(s):  
Burgers Equation ◽  
Higher Order ◽  
Underlying Structure ◽  
Swarm Dynamics ◽  
Special Cases ◽  
Kink Waves ◽  
Systematic Derivation ◽  
Fifth Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.

Rogue wave solutions for the higher-order nonlinear Schrödinger equation with variable coefficients by generalized Darboux transformation

2016 ◽  
Vol 30 (10) ◽  
pp. 1650106 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Jian Chen
Keyword(s):  
Darboux Transformation ◽  
Variable Coefficient ◽  
Rogue Wave ◽  
Variable Coefficients ◽  
Higher Order ◽  
Optical Systems ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Order Variable ◽  
Generalized Darboux Transformation

In this paper, we study a higher-order variable coefficient nonlinear Schrödinger (NLS) equation, which plays an important role in the control of the ultrashort optical pulse propagation in nonlinear optical systems. Then, we construct a generalized Darboux transformation (GDT) for the higher-order variable coefficient NLS equation. The [Formula: see text]th order rogue wave solution is obtained by the iterative rule and it can be expressed by the determinant form. As application, we calculate rogue waves (RWs) from first- to fourth-order in accordance with different kinds of parameters. In particular, the dynamical properties and spatial-temporal structures of RWs are discussed and compared with Hirota equation through some figures.

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.

Dark soliton dynamics for quantum systems with higher-order dispersion and higher-order nonlinearity

2021 ◽  
pp. 2150284
Author(s):  
Chen Chen ◽  
Guojun Gao ◽  
Ying Wang ◽  
Yuqi Pan ◽  
Shuyu Zhou
Keyword(s):  
Soliton Solution ◽  
Dark Soliton ◽  
Quantum Systems ◽  
Higher Order ◽  
High Order ◽  
Nonlinear Interactions ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One ◽  
Order Dispersion

In this work, we investigated one-dimensional and two-dimensional quantum systems with higher-order dispersions and higher-order nonlinear interactions. Based on the high-order nonlinear Schrödinger equation (NLSE) and via the [Formula: see text]-expansion method, we derived the analytical dark soliton solution for the one-dimensional system first. By applying the self-similar method and using the results of the one-dimensional case, the analytical dark soliton solution of the system in the two-dimensional case was derived. The dynamic evolution pattern of the two-dimensional dark soliton is pictorially demonstrated. The theoretical results of our work can be used to guide the detection and experimental study of dark soliton in a two-dimensional quantum system, using high-order dispersion and higher-order nonlinear interactions.

scholarly journals Contribution of Higher-Order Dispersion to Nonlinear Dust Ion Acoustic Waves in Inhomogeneous Mesospheric Dusty Plasma with Dust Charge Fluctuation

2010 ◽  
Vol 65 (1-2) ◽  
pp. 91-99 ◽  
Author(s):  
Mohamed T. Attia ◽  
Mohsen A. Zahran ◽  
Emad K. El-Shewy ◽  
Ahmed E. Mowafy
Keyword(s):  
Dusty Plasma ◽  
Acoustic Waves ◽  
Kdv Equation ◽  
Variable Coefficients ◽  
Higher Order ◽  
Ion Acoustic Waves ◽  
Dust Charge ◽  
Ion Acoustic ◽  
Dust Ion Acoustic Waves ◽  
Order Dispersion

AbstractThe propagation of dust ion acoustic waves (DIAWs) in a weakly inhomogeneous, weakly coupled, collisionless, and unmagnetized four components dusty plasma are examined. The fluid system considered in this work consists of cold positive ions, cold negatively and positively charged dust particles associated with isothermal electrons. For nonlinear (DIAW) waves, a reductive perturbation method was employed to obtain the variable coefficients Kortewege-de Vries (KdV) equation for the first-order potential. For local inhomogenity, the present system admits the coexistence of rarefactive and compressive solitons. As a matter of fact, when the wave amplitude enlarged, the width and velocity of the wave deviate from the prediction of the KdV equation. It means that we have to extend our analysis to obtain the variable coefficients Kortewege-de Vries (KdV) equation with fifth-order dispersion term. For locally constant parameters, the higher-order solution for the resulting equation has been achieved via what is called perturbation technique. The effects of positive and negative dust charge fluctuations on the higher-order soliton amplitude and width of electrostatic solitary structures are outlined.

Dark solitons for a variable-coefficient higher-order nonlinear Schrödinger equation in the inhomogeneous optical fiber

2017 ◽  
Vol 31 (12) ◽  
pp. 1750065 ◽  
Author(s):  
Yan Sun ◽  
Bo Tian ◽  
Xiao-Yu Wu ◽  
Lei Liu ◽  
Yu-Qiang Yuan
Keyword(s):  
Schrödinger Equation ◽  
Optical Fiber ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Dark Solitons ◽  
Order Dispersion

Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with [Formula: see text], [Formula: see text] and [Formula: see text], which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to [Formula: see text], [Formula: see text] and [Formula: see text], respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.

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