scholarly journals SOLITON SOLUTIONS OF THE GENERALIZED NONLINEAR SCHR?DINGER EQUATION WITH HIGHER-ORDER CORRECTIONS BY THE DIRECT METHOD OF HIROTA

1991 ◽  
Vol 40 (1) ◽  
pp. 1
Author(s):  
LIU ZHONG-ZHU ◽  
HUANG NIAN-NING
Keyword(s):  
Direct Method ◽  
Soliton Solutions ◽  
Higher Order ◽  
Dinger Equation ◽  
Higher Order Corrections

scholarly journals N-soliton solutions and the Hirota conditions in (1 + 1)-dimensions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wen-Xiu Ma
Keyword(s):  
Common Factors ◽  
Soliton Solutions ◽  
Higher Order ◽  
Kdv Equations ◽  
The Common ◽  
Bilinear Formulation ◽  
Generalized Kdv Equations ◽  
Hirota Bilinear

Abstract We analyze N-soliton solutions and explore the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations, within the Hirota bilinear formulation. An algorithm to verify the Hirota conditions is proposed by factoring out common factors out of the Hirota function in N wave vectors and comparing degrees of the involved polynomials containing the common factors. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, together with all proofs of the existence of N-soliton solutions to all equations in two classes.

Some applications of the revisited approximate next-to-leading higher order corrections in QCD

2015 ◽  
Vol 30 (11) ◽  
pp. 1550047
Author(s):  
N. Mebarki ◽  
M. R. Bekli ◽  
H. Aissaoui
Keyword(s):  
Higher Order ◽  
Higher Order Corrections

Using the prescription and techniques of the soft and/or collinear gluon approach developed in Refs. 1–5 and revisited in Ref. 6, applications to some hadronic subprocesses are considered and approximate QCD higher order contributions are determined.

Tunnelling Effects of Solitons in Optical Fibers with Higher-Order Effects

2012 ◽  
Vol 67 (6-7) ◽  
pp. 338-346
Author(s):  
Chao-Qing Dai ◽  
Hai-Ping Zhu ◽  
Chun-Long Zheng
Keyword(s):  
Optical Fibers ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Order Effects ◽  
Bright Solitons ◽  
Dark Solitons ◽  
Tunnelling Effect ◽  
Tunnelling Effects ◽  
Higher Order Effects

We construct four types of analytical soliton solutions for the higher-order nonlinear Schrödinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly.We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons

Interplay Between Dispersion and Nonlinearity in Femtosecond Soliton Management

2010 ◽  
Vol 65 (6-7) ◽  
pp. 549-554
Author(s):  
Ramaswamy Radha ◽  
Vaduganathan Ramesh Kumar
Keyword(s):  
Pulse Propagation ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Higher Order ◽  
Order Effects ◽  
Nls Equation ◽  
Linear Eigenvalue Problem ◽  
Third Order Dispersion ◽  
Femtosecond Regime ◽  
Soliton Management

In this paper, we investigate the inhomogeneous higher-order nonlinear Schr¨odinger (NLS) equation governing the femtosecond optical pulse propagation in inhomogeneous fibers using gauge transformation and generate bright soliton solutions from the associated linear eigenvalue problem. We observe that the amplitude of the bright solitons depends on the group velocity dispersion (GVD) and the self-phase modulation (SPM) while its velocity is dictated by the third-order dispersion (TOD) and GVD. We have shown how the interplay between GVD, SPM, and TOD can be profitably exploited to change soliton width, amplitude (intensity), shape, phase, velocity, and energy for an effective femtosecond soliton management. The highlight of our paper is the identification of ‘optical similaritons’ arising by virtue of higher-order effects in the femtosecond regime.

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