Volume 28, Issue 2
A New Jacobi Elliptic Function Expansion Method for Solvinga Nonlinear PDE Describing Pulse Narrowing Nonlinear Transmission Lines

Elsayed M. E. Zayed & K. A. E. Alurrfi

J. Part. Diff. Eq., 28 (2015), pp. 128-138.

Published online: 2015-06

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  • Abstract

In this article, we apply the first elliptic function equation to find a new kind of solutions of nonlinear partial differential equations (PDEs) based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method. New exact solutions to the Jacobi elliptic functions of a nonlinear PDE describing pulse narrowing nonlinear transmission lines are given with the aid of computer program, e.g. Maple or Mathematica. Based on Kirchhoff's current law and Kirchhoff's voltage law, the given nonlinear PDE has been derived and can be reduced to a nonlinear ordinary differential equation (ODE) using a simple transformation. The given method in this article is straightforward and concise, and can be applied to other nonlinear PDEs in mathematical physics. Further results may be obtained.

  • Keywords

New Jacobi elliptic function expansion method pulse narrowing nonlinear transmission lines exact solutions Kirchhoff's current law Kirchhoff's voltage law

  • AMS Subject Headings

35K99, 35P05, 35P99, 35C05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

e.m.e.zayed@hotmail.com (Elsayed M. E. Zayed)

alurrfi@yahoo.com (K. A. E. Alurrfi)

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  • RIS
  • TXT
@Article{JPDE-28-128, author = {Zayed , Elsayed M. E. and Alurrfi , K. A. E. }, title = {A New Jacobi Elliptic Function Expansion Method for Solvinga Nonlinear PDE Describing Pulse Narrowing Nonlinear Transmission Lines}, journal = {Journal of Partial Differential Equations}, year = {2015}, volume = {28}, number = {2}, pages = {128--138}, abstract = { In this article, we apply the first elliptic function equation to find a new kind of solutions of nonlinear partial differential equations (PDEs) based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method. New exact solutions to the Jacobi elliptic functions of a nonlinear PDE describing pulse narrowing nonlinear transmission lines are given with the aid of computer program, e.g. Maple or Mathematica. Based on Kirchhoff's current law and Kirchhoff's voltage law, the given nonlinear PDE has been derived and can be reduced to a nonlinear ordinary differential equation (ODE) using a simple transformation. The given method in this article is straightforward and concise, and can be applied to other nonlinear PDEs in mathematical physics. Further results may be obtained.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v28.n2.3}, url = {http://global-sci.org/intro/article_detail/jpde/5106.html} }
TY - JOUR T1 - A New Jacobi Elliptic Function Expansion Method for Solvinga Nonlinear PDE Describing Pulse Narrowing Nonlinear Transmission Lines AU - Zayed , Elsayed M. E. AU - Alurrfi , K. A. E. JO - Journal of Partial Differential Equations VL - 2 SP - 128 EP - 138 PY - 2015 DA - 2015/06 SN - 28 DO - http://doi.org/10.4208/jpde.v28.n2.3 UR - https://global-sci.org/intro/article_detail/jpde/5106.html KW - New Jacobi elliptic function expansion method KW - pulse narrowing nonlinear transmission lines KW - exact solutions KW - Kirchhoff's current law KW - Kirchhoff's voltage law AB - In this article, we apply the first elliptic function equation to find a new kind of solutions of nonlinear partial differential equations (PDEs) based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method. New exact solutions to the Jacobi elliptic functions of a nonlinear PDE describing pulse narrowing nonlinear transmission lines are given with the aid of computer program, e.g. Maple or Mathematica. Based on Kirchhoff's current law and Kirchhoff's voltage law, the given nonlinear PDE has been derived and can be reduced to a nonlinear ordinary differential equation (ODE) using a simple transformation. The given method in this article is straightforward and concise, and can be applied to other nonlinear PDEs in mathematical physics. Further results may be obtained.
Elsayed M. E. Zayed & K. A. E. Alurrfi. (2019). A New Jacobi Elliptic Function Expansion Method for Solvinga Nonlinear PDE Describing Pulse Narrowing Nonlinear Transmission Lines. Journal of Partial Differential Equations. 28 (2). 128-138. doi:10.4208/jpde.v28.n2.3
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