Analytical and soliton solutions: Nonlinear model of nanobioelectronics transmission lines

2015 ◽  
Vol 265 ◽  
pp. 994-1002 ◽  
Author(s):  
Muhammad Younis ◽  
Syed Tahir Raza Rizvi ◽  
Safdar Ali
Keyword(s):  
Nonlinear Model ◽  
Transmission Lines ◽  
Soliton Solutions

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.

scholarly journals Wave Propagations in Nonlinear Low-Pass Electrical Transmission Lines through Optical Fiber Medium

2022 ◽  
Vol 2022 ◽  
pp. 1-16
Author(s):  
Aniqa Zulfiqar ◽  
Jamshad Ahmad ◽  
Attia Rani ◽  
Qazi Mahmood Ul Hassan
Keyword(s):  
Transmission Lines ◽  
Model Equation ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Electrical Transmission ◽  
Low Pass ◽  
Physical Importance ◽  
Complex Phenomena ◽  
Soliton Wave Solutions

The present article discovers the new soliton wave solutions and their propagation in nonlinear low-pass electrical transmission lines (NLETLs). Based on an innovative Exp-function method, multitype soliton solutions of nonlinear fractional evolution equations of NLETLs are established. The equation is reformulated to a fractional-order derivative by using the Jumarie operator. Some new results are also presented graphically to understand the real physical importance of the studied model equation. The physical interpretation of waves is represented in the form of three-dimensional and contour graphs to visualize the underlying dynamic behavior of these solutions for particular values of the parameters. Moreover, the attained outcomes are generally new for the considered model equation, and the results show that the used method is efficient, direct, and concise which can be used in more complex phenomena.

Wave propagation of the perturbed nonlinear Schrödingers equation in the nonlinear left-handed transmission lines

2018 ◽  
Vol 13 (02) ◽  
pp. 2050035 ◽  
Author(s):  
Alphonse Houwe ◽  
Mibaile Justin ◽  
Dikwa Jérôme ◽  
Gambo Betchewe ◽  
Serge Y. Doka ◽  
...  
Keyword(s):  
Transmission Lines ◽  
Soliton Solutions ◽  
Efficient Solutions ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Ansatz Method ◽  
Auxiliary Equation Method ◽  
Left Handed ◽  
Existence Criteria ◽  
Parabolic Law Nonlinearity

This paper secures chirped dark and bright solitons of the perturbed nonlinear Schrödinger equation with parabolic law nonlinearity and self-steepening effect in the nonlinear left-handed metamaterials (NLHMs). We use the ansatz method, sine-cosine, csch function method and the auxiliary equation method to fall out the various soliton solutions. In view of the results obtained, rational, hyperbolic and trigonometric solutions emerge and there are new in CRLH TL. The existence criteria of these solutions are also discussed. Finally, we observed that the use of the auxiliary equation method leads to the abundant and efficient solutions than the other methods.

On the Complex Simulations With Dark–Bright to the Hirota–Maccari System

2021 ◽  
Vol 16 (6) ◽  
Author(s):  
Gulnur Yel ◽  
Carlo Cattani ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Nonlinear Model ◽  
Analytical Approach ◽  
Gordon Equation ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Two Dimensional

Abstract This paper investigates the coupled nonlinear Hirota–Maccari system with the help of using an analytical approach, which is the extended sinh-Gordon equation expansion method (ShGEEM). Complex, solitary, and singular periodic traveling solutions are successfully gained to the nonlinear model considered. The constraint conditions that validate the existence of the reported soliton solutions are also given in a detailed manner. The two-dimensional (2D), three-dimensional, and contour graphs to some of the obtained solutions are presented via several computational programs. These simulations present deeper investigations about the wave distributions of the coupled nonlinear Hirota–Maccari system.

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