Higher-order algebraic soliton solutions of the Gerdjikov-Ivanov equation: Asymptotic analysis and emergence of rogue waves

2021 ◽  
pp. 133128
Author(s):  
Shan-Shan Zhang ◽  
Tao Xu ◽  
Min Li ◽  
Xue-Feng Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Higher Order ◽  
Order Algebraic

Dynamical interactions between higher-order rogue waves and various forms of n-soliton solutions (n → ∞) of the (2+1)-dimensional ANNV equation

2020 ◽  
Vol 29 (11) ◽  
pp. 114701 ◽  
Author(s):  
Md Fazlul Hoque ◽  
Harun-Or-Roshid ◽  
Fahad Sameer Alshammari
Keyword(s):  
Soliton Solutions ◽  
Rogue Waves ◽  
Higher Order

Inverse scattering method for the Kundu-Eckhaus equation with zero/nonzero boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Guixian Wang ◽  
Xiu-Bin Wang ◽  
Bo Han ◽  
Qi Xue
Keyword(s):  
Boundary Conditions ◽  
Inverse Scattering ◽  
Hilbert Problem ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Higher Order ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Nonzero Boundary ◽  
Wave Phenomena

Abstract In this paper, the inverse scattering approach is applied to the Kundu-Eckhaus equation with two cases of zero boundary condition (ZBC) and nonzero boundary conditions (NZBCs) at infinity. Firstly, we obtain the exact formulae of soliton solutions of three cases of N simple poles, one higher-order pole and multiple higher-order poles via the associated Riemann-Hilbert problem (RHP). Moreover, given the initial data that allow for the presence of discrete spectrum, the higher-order rogue waves of the equation are presented. For the case of NZBCs, we can construct the infinite order rogue waves through developing a suitable RHP. Finally, by choosing different parameters, we aim to show some prominent characteristics of this solution and express them graphically in detail. Our results should be helpful to further explore and enrich the related nonlinear wave phenomena.

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.

The Higher Order Asymptotic Fields for Plane Interfacial Crack with Physical Weak-Discontinuity

2011 ◽  
Vol 217-218 ◽  
pp. 1314-1318
Author(s):  
Yao Dai ◽  
Lei Zhang ◽  
Peng Zhang ◽  
Jun Feng Liu
Keyword(s):  
Experimental Investigation ◽  
Numerical Analysis ◽  
Asymptotic Analysis ◽  
Theoretical Basis ◽  
Engineering Application ◽  
Interfacial Crack ◽  
Higher Order ◽  
Weak Discontinuity ◽  
Displacement Method ◽  
Asymptotic Fields

The higher order discontinuous asymptotic fields which are similar to the Williams’ solutions of homogenous material are obtained by the displacement method and asymptotic analysis for a plane crack at the physical weak-discontinuous interface in non-homogeneous materials. The results provide a theoretical basis for the numerical analysis, experimental investigation and the engineering application of physical weak-discontinuous fracture.

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.

Rogue waves in higher-order systems: Lagrangian approach

2019 ◽  
Vol 94 (3) ◽  
pp. 035203
Author(s):  
Mahyar Bokaeeyan ◽  
Adrian Ankiewicz ◽  
Nail Akhmediev
Keyword(s):  
Rogue Waves ◽  
Higher Order ◽  
Lagrangian Approach
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