Traveling and localized solitary wave solutions of the nonlinear electrical transmission line model equation
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Traveling and localized solitary wave solutions of the nonlinear electrical transmission line model equation Hitender Kumar1,a
, Shoukry El-Ganaini2
1 Department of Physics, Pt. Neki Ram Sharma Government College, Rohtak, Haryana 124001, India 2 Faculty of Science, Department of Mathematics, Damanhour University, Bahira 22514, Egypt
Received: 29 May 2020 / Accepted: 3 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Analytical solutions describing the kink–antikink type, hyperbolic, trigonometric, doubly periodic, localized bright and dark soliton like, breather and rational periodic train solutions to the discrete nonlinear electrical transmission line in (2+1)-dimensions have been investigated with the Kudryashov method, the fractional linear transform method, and the simplest equation method with its modified and extended versions. Consequently, many new and more general explicit forms of traveling waves are retrieved under parametric conditions. The 3D, 2D, and density profile of some of the obtained results are numerically simulated by selecting suitable values of the various parameters of the NLTL model equation. Furthermore, all the obtained results were checked and verified by putting back into the considered nonlinear transmission line model equation with Maple and Mathematica software. The acquired results show the validity and reliability of the proposed schemes to the studied nonlinear electrical transmission line model.
1 Introduction The study of nonlinear dynamical systems is presently a very intense topic of research, in which nonlinear equations are analytically treated by a variety of methods to gain a deeper understanding and knowledge of the formation of localized solitary wave trains and traveling waves. The concept of solitons characterizes the prominent and well-known aspects of nonlinear phenomena in spatially extended integrable systems. The moving solitons carrying energy in a coherent and particle-like model for integrable systems and emerge as special sorts of localized solutions of nonlinear evolution equations and preserve many significant properties such as elastic scattering and exponential localization of energy which remain stable during soliton communication. The nonlinear evolution equations are widely acknowledged as models to illustrate complex physical phenomena in several disciplines of sciences such as physics, fluid dynamics, optical telecommunications, biology, chemistry, and mechanics [1,2]. To find analytical solutions of such soliton complexes is a challenging task and is considered desirable, from the theoretical point of view. Although several numerical schemes can resolve these equations numerically so that it is likely to visualize
a e-mail: [email protected] (corresponding author)
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the solution but a closed-form exact solution is still necessary for a systematic study of the properties of the solitons. Accor
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