scholarly journals Dynamics of bright and dark multi-soliton solutions for two higher-order Toda lattice equations for nonlinear waves

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Nan Liu ◽  
Xiao-Yong Wen ◽  
Ling Xu
Keyword(s):  
Nonlinear Waves ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Higher Order ◽  
Toda Lattice Equations

scholarly journals Explicit Solutions of Integrable Variable-coeffcient Cylindrical Toda Equations

2020 ◽  
pp. 1-9
Author(s):  
Ting Su ◽  
Jia Wang ◽  
Quan Zhen Huang
Keyword(s):  
Soliton Solution ◽  
Compatibility Condition ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Explicit Solutions ◽  
Dressing Method ◽  
New Type ◽  
Toda Equations ◽  
Toda Lattice Equations

Integrable cylindrical Toda lattice equations are proposed by utilizing a generalized version of the dressing method. A compatibility condition is given which insures that these equations are integrable. Further, soliton solutions for new type equations are shown in explicit forms, including one soliton solution and two soliton solutions, respectively.

scholarly journals Extended Mixed Function Method and Its Application for Solving Two Classic Toda Lattice Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-24
Author(s):  
Weiguo Rui ◽  
Xinsong Yang
Keyword(s):  
Exact Solution ◽  
Function Method ◽  
Toda Lattice ◽  
Dynamic Properties ◽  
Dimensional Space ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Discrete Breather ◽  
Wave Solutions ◽  
Toda Lattice Equations

The mixed function method is extended from the(1+1)-dimensional space to the(2+1)-dimensional one, even those forms of exact solution do not exist in(1+1)-dimensional NDDEs. By using this extended method, the Toda lattice and(2+1)-dimensional Toda lattice equations are studied. Some new solutions such as discrete solitary wave solutions, discrete kink and antikink wave solutions, and discrete breather soliton solutions are obtained, and their dynamic properties are discussed.

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.

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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