Algebraic Method for Constructing Exact Discrete Soliton Solutions of Toda and mKdV Lattices

2008 ◽  
Vol 49 (6) ◽  
pp. 1407-1409 ◽  
Author(s):  
Wang Jun-Min ◽  
Ji Jie
Keyword(s):  
Soliton Solutions ◽  
Algebraic Method ◽  
Discrete Soliton

An explicit plethora of soliton solutions for a new microtubules transmission lines model: A fractional comparison

2021 ◽  
Author(s):  
Nauman Raza ◽  
Ziyad A. Alhussain
Keyword(s):  
Nonlinear Dynamics ◽  
Transmission Lines ◽  
Fractional Derivatives ◽  
Intracellular Transport ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Governing System ◽  
Parameter Values ◽  
Fractional Parameter

This paper introduces a new fractional electrical microtubules transmission lines model in the sense of Atangana–Baleanu and beta derivatives to comprehend nonlinear dynamics of the governing system. This structure possesses one of the most important parts in cellular process biology and fractional parameter incorporates the memory effects in microtubules. Also, microtubules are extremely beneficial in cell motility, signaling and intracellular transport. The new extended direct algebraic method is a compelling and persuasive integrating scheme to extract soliton solutions. The retrieved solutions include dark, bright and singular solitons. This model executes a prominent part in exhibiting the wave transmission in nonlinear systems. The novelty and advantage of the proposed method are portrayed by applying it to this model and its dynamical behavior is depicted by 3D and 2D plots. A comparative study of two fractional derivatives at distinct fractional parameter values and graphics of sensitivity analysis is also carried out in this paper.

Highly dispersive optical soliton perturbation with cubic–quintic–septic law via two methods

2021 ◽  
pp. 2150276
Author(s):  
Khalid K. Ali ◽  
Hadi Rezazadeh ◽  
Nauman Raza ◽  
Mustafa Inc
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Optical Solitons ◽  
Optical Soliton ◽  
Mixed Complex ◽  
Solitary Wave Solutions ◽  
Computational System ◽  
Soliton Perturbation ◽  
Wave Solutions

The main consideration of this paper is to discuss cubic optical solitons in a polarization-preserving fiber modeled by nonlinear Schrödinger equation (NLSE). We extract the solutions in the forms of hyperbolic, trigonometric including a class of solitary wave solutions like dark, bright–dark, singular, singular periodic, multiple-optical soliton and mixed complex soliton solutions. A recently developed integration tool known as new extended direct algebraic method (NEDAM) is applied to analyze the governing model. Moreover, the studied equation is discussed with two types of nonlinearity. The constraint conditions are explicitly presented for the resulting solutions. The accomplished results show that the applied computational system is direct, productive, reliable and can be carried out in more complicated phenomena.

Exact discrete soliton solutions of the nonlinear differential-difference equations

2007 ◽  
Vol 34 (3) ◽  
pp. 940-946 ◽  
Author(s):  
Xiao-Fei Wu ◽  
Hong-Liang Ge ◽  
Zheng-Yi Ma
Keyword(s):  
Difference Equations ◽  
Soliton Solutions ◽  
Discrete Soliton

Optical dark and singular solitons of generalized nonlinear Schrödinger’s equation with anti-cubic law of nonlinearity

2019 ◽  
Vol 33 (13) ◽  
pp. 1950158 ◽  
Author(s):  
Nauman Raza ◽  
Asad Zubair
Keyword(s):  
Optical Fibers ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Rational Solutions ◽  
Schrödinger’S Equation ◽  
Light Pulses ◽  
Propagation Of Light ◽  
Schrödinger's Equation ◽  
Nonlinear Schrodinger’S Equation ◽  
Nonlinear Schrödinger’S Equation

This work is devoted to scrutinize new optical soliton solutions to the spatially temporal [Formula: see text]-dimensional nonlinear Schrödinger’s equation (NLSE) with anti-cubic nonlinearity. Two different versatile integration architectures are used to extract these solitons. Extended direct algebraic method (EDAM) is utilized to pluck out optical, dark and singular soliton solutions, whereas generalized Kudryashov method (GKM) provides rational solutions. The fetched results are new and useful for the propagation of light pulses in optical fibers in [Formula: see text]-dimensions. For the existence of these solitons, constraint conditions are also listed.

Uniformly Constructing a Series of Nonlinear Wave and Coefficient Functions’ Soliton Solutions and Double Periodic Solutions for the (2 + 1)-Dimensional Broer-Kaup-Kupershmidt Equation

2005 ◽  
Vol 60 (3) ◽  
pp. 127-138
Author(s):  
Yong Chen ◽  
Qi Wang ◽  
Yanghuai Lang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Symbolic Computation ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Extended Tanh Method ◽  
Tanh Method

By using a new more general ansatz with the aid of symbolic computation, we extended the unified algebraic method proposed by Fan [Computer Phys. Commun. 153, 17 (2003)] and the improved extended tanh method by Yomba [Chaos, Solitons and Fractals 20, 1135 (2004)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations. The efficiency of the method is demonstrated on the (2+1)-dimensional Broer-Kaup- Kupershmidt equation.

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