A third-order nonlinear Schrodinger equation: the exact solutions, group-invariant solutions and conservation laws


SAĞLAM ÖZKAN Y., YAŞAR E., Seadawy A. R.

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, vol.14, no.1, pp.585-597, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1080/16583655.2020.1760513
  • Journal Name: JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.585-597
  • Keywords: Optical travelling wave solutions, Schrodinger equation, the extended modified method, DISPERSIVE DIELECTRIC FIBERS, OPTICAL SOLITON-SOLUTIONS, TRANSMISSION, BRIGHT, PULSES
  • Bursa Uludag University Affiliated: Yes

Abstract

In this study, we consider the third order nonlinear Schrodinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. With the help of the extended modified method, we obtain numerous exact travelling wave solutions containing sets of generalized hyperbolic, trigonometric and rational solutions that are more general than classical ones. Secondly, we construct the transformation groups which left the equations invariant and vector fields with the Lie symmetry groups approach. With the help of these vector fields, we obtain the symmetry reductions and exact solutions of the equation. The obtained group-invariant solutions are Jacobi elliptic function and exponential type. We discuss the dynamic behaviour and structure of the exact solutions for distinct solutions of arbitrary constants. Lastly, we obtain conservation laws of the considered equation by construing the complex equation as a system of two real partial differential equations (PDEs).