Modeling Nonlinear Partial Differential Equations and Construction of Solitary Wave Solutions in an Inductive Electrical Line
Journal of Advances in Mathematics and Computer Science,
A soliton is considered nowadays as a future wave reason being the fact that it is a stable, robust and non-dissipative solitary wave. If one uses a soliton as a transmission signal in electrical lines, this will have a great impacts in the domain of economic, technology and education. Given the fact that the propagation of the soliton is due to the interaction between dispersion and nonlinearity, it necessitates that the transmission medium should be dispersive and nonlinear. The physical system we have chosen for our survey is an inductive electrical line reason being the fact that it is the cheapest and very easy to manufacture than any other transmission lines; furthermore we find out the analytical variation that the magnetic flux linkage of inductors in the electrical line must undergo so that its transmission medium admits the propagation of solitary waves of required type. The aim of this work is to model nonlinear partial differential equations which govern the dynamics of those solitary waves in the line, to define the analytical expression of the magnetic flux linkage of inductors in the line and to find out some exact solutions of solitary waves types of those equations. To meet our objectives, we apply Kirchhoff laws to the circuit of a nonlinear inductive electrical line to model the nonlinear partial differential equation which describe the dynamics of those solitons. Further we apply the effective and direct Bogning-Djeumen Tchaho-Kofane method based on the identification of basic hyperbolic function coefficients to construct some exact soliton solutions of modeled equations. Numerical simulations have enabled to draw and observe the real profile of those solitary waves which are Kink soliton and Pulse soliton. The obtained results are supposed to permits: The facilitation of the choice of the type of line relative to the type of signal one wishes to send across, to increase the mathematical field knowledge, the reduction of amplification stations of those lines, The manufacturing of new inductors and new electrical lines susceptible of propagating those solitary waves.
- Inductive electrical line
- soliton solution
- solitary wave
- nonlinear partial differential equation
How to Cite
Numerical treatment of fractional order Cauchy reaction diffusion equations. Chaos, Solitons and Fractals. 2017;103:578-587.
Numerical treatment for traveling wave solutions of fractional Whitham-Broer-Kaup equations. Alexandria Engineering Journal; 2017.
Abdelrahman MAE, Sohaly MA. Solitary waves for the modified Korteweg-De Vries equation in deterministic case and random case. J Phys Math. 2017;8(1).
Abdelrahman MAE, Sohaly MA. Solitary waves for the nonlinear Schrodinger problem with the probability distribution function in stochastic input case. Eur. Phys. J. Plus; 2017.
Abdelrahman MAE. A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations. Nonlinear Engineering Modeling and Application; 2018.
Singh J, Kumar D, Baleanu D. An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation. Applied Mathematics and Computation. 2018;335:12-24.
Wazwaz AM. The tanh-coth method for new compactons and solitons solutions for the K(n,n) and K(n+1, n+1) equations, persive K(m,n) equations. Appl. Math. Comput. 2007;188:1930-1940.
Wang ML. Exact solutions for a compound Käv- Burgers equation. Phys. Lett. A. 1996;213:279-287.
Fan E. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A. 2000;277:212-218.
Fan E, Zhang J. A note on the homogeneous balance method. Phys. Lett. A. 2002;305:383-392.
Zhou YB, Wang ML, Wang YM. Periodic wave solutions to a coupled KdV equations with variable coefficients. Phys. Lett. A. 2003;308:31-37.
Wazwaz AM. Solutions of compact and non compact structures for nonlinear Klein-Gordon type equation. Appl. Math. Comput. 2003;134:487-500.
Wazwaz AM. Traveling wave solutions of generalized forms of Burgers – KdV and Burgers Huxly equations. Appl. Math. Comput. 2005;169:639-656.
Feng Z. The first integral method to study the Burgers – Korteweg-de-Vries equation. J. Phys. Lett. A. 2002;35:343-349.
Feng Z. On explicit exat solutions for the Lienard equation and its applications. J. Phys. Lett. A. 2002;293:57-66.
Feng Z. On explicit exact solutions to compound Burgers- KdV equation. J. Math. Anal. Appl. 2007;328:1435-1450.
Bogning JR, Djeumen Tchaho CT, Kofané TC. Construction of the soliton solutions of the Ginzburg-Landau equations by the new Bogning-Djeumen Tchaho-Kofané method. Phys. Scr. 2012;85:025013-025017.
Bogning JR, Djeumen Tchaho CT, Kofané TC. Generalization of the Bogning- Djeumen Tchaho-Kofane method for the construction of the solitary waves and the survey of the instabilities. Far East J. Dyn. Sys. 2012;20(2):101-119.
Djeumen Tchaho CT, Bogning JR, Kofané TC. Modulated soliton solution of the modified Kuramoto-Sivashinsky's equation. American Journal of Computational and Applied Mathematics. 2012;2(5): 218-224.
Djeumen Tchaho CT, Bogning JR, Kofane TC. Multi-soliton solutions of the modified Kuramoto-Sivashinsky’s equation by the BDK method. Far East J. Dyn. Sys. 2011;15(2):83-98.
Djeumen Tchaho CT, Bogning JR, Kofane TC. Construction of the analytical solitary wave solutions of modified Kuramoto-Sivashinsky equation by the method of identification of coefficients of the hyperbolic functions. Far East J. Dyn. Sys. 2010;14(1):14-17.
Bogning JR. Pulse soliton solutions of the modified KdV and Born-Infeld equations. International Journal of Modern Nonlinear Theory and Application. 2013;2:135-140.
Abstract View: 1660 times
PDF Download: 659 times