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Volume 28, Issue 4
Exact Traveling Wave Solutions for Higher Order Nonlinear Schrödinger Equations in Optics by Using the (G'/G, 1/G)-expansion Method

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

DOI: 10.4208/jpde.v28.n4.4

J. Part. Diff. Eq., 28 (2015), pp. 332-357.

Published online: 2015-12

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  • Abstract
The propagation of the optical solitons is usually governed by the nonlinear Schrödinger equations. In this article, the two variable (G'/G, 1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear Schrödinger equations describing the propagation of femtosecond pulses in nonlinear optical fibers. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations rediscovered from the traveling waves. Thismethod can be thought of as the generalization of well-known original (G'/G)-expansion method proposed by M. Wang et al. It is shown that the two variable (G'/G, 1/G)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics.
  • Keywords

The two variable (G'⁄G 1⁄G)-expansion method Schrödinger equations exact traveling wave solutions solitary wave solutions

  • AMS Subject Headings

35Q51, 37K10, 35K99, 35P05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

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

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

  • BibTex
  • RIS
  • TXT
@Article{JPDE-28-332, author = {Zayed , Elsayed M. E. and Alurrfi , K. A. E.}, title = {Exact Traveling Wave Solutions for Higher Order Nonlinear Schrödinger Equations in Optics by Using the (G'/G, 1/G)-expansion Method}, journal = {Journal of Partial Differential Equations}, year = {2015}, volume = {28}, number = {4}, pages = {332--357}, abstract = { The propagation of the optical solitons is usually governed by the nonlinear Schrödinger equations. In this article, the two variable (G'/G, 1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear Schrödinger equations describing the propagation of femtosecond pulses in nonlinear optical fibers. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations rediscovered from the traveling waves. Thismethod can be thought of as the generalization of well-known original (G'/G)-expansion method proposed by M. Wang et al. It is shown that the two variable (G'/G, 1/G)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v28.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/5120.html} }
TY - JOUR T1 - Exact Traveling Wave Solutions for Higher Order Nonlinear Schrödinger Equations in Optics by Using the (G'/G, 1/G)-expansion Method AU - Zayed , Elsayed M. E. AU - Alurrfi , K. A. E. JO - Journal of Partial Differential Equations VL - 4 SP - 332 EP - 357 PY - 2015 DA - 2015/12 SN - 28 DO - http://doi.org/10.4208/jpde.v28.n4.4 UR - https://global-sci.org/intro/article_detail/jpde/5120.html KW - The two variable (G'⁄G KW - 1⁄G)-expansion method KW - Schrödinger equations KW - exact traveling wave solutions KW - solitary wave solutions AB - The propagation of the optical solitons is usually governed by the nonlinear Schrödinger equations. In this article, the two variable (G'/G, 1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear Schrödinger equations describing the propagation of femtosecond pulses in nonlinear optical fibers. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations rediscovered from the traveling waves. Thismethod can be thought of as the generalization of well-known original (G'/G)-expansion method proposed by M. Wang et al. It is shown that the two variable (G'/G, 1/G)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics.
Elsayed M. E. Zayed & K. A. E. Alurrfi. (2019). Exact Traveling Wave Solutions for Higher Order Nonlinear Schrödinger Equations in Optics by Using the (G'/G, 1/G)-expansion Method. Journal of Partial Differential Equations. 28 (4). 332-357. doi:10.4208/jpde.v28.n4.4
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