Keywords:-
Article Content:-
Abstract
We considered the third order nonlinear Schrodinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. We extended modified sub-equation method to obtain numerous exact travelling wave solutions containing sets of generalized hyperbolic. Trigonometric and rational solutions that are more general than classical ones. We followed analytical mathematical metod by constructed the transformation groups which help us using vector fields and Lie symmetry groups. We discussed the dynamic behavior and structure of the exact solutions for distinct solution of arbitrary constants .We obtained the symmetry reductions and exact of the equation. In addition to group-invariant solutions which are Jacobi elliptic function and exponential type.
References:-
References
Hasegawa A, Tppert F. Transmission of Stationary nonlinear Optical Pulses in dispersive fibers. I. Anomalous Appl Phys Lett 1973;23(3):142-144.
Bulut H,Sulaiman TA, Baskonus HM, et al. Optical Solutions to the comfortable Space-time fractional Fokas-lenells equation Optik. 2018,172:20-27.
Arshed, S, Biswas, A, Abdelaty M, et al. Optical solution perturbation of Gerdjikov-Lvanov equation via two analytical techniques. Chines, J Phys. 2018;56(6):2879-2886.
Li BQ, Sun JZ. Ma YL. Soliton excitation for a coherently coupled nonlinear Schro ̈dinger system in optical fibers with two orthogonally polarized components. Optik.2018;175-283.
Guna X, Liu W. Zhon Q et al. Some lum solusev-petviashvili equation. Appl Math comput. 2020;366:124757.
Guan X, Zhou Q,, Liu W. Lump and lump strip solutions to the (3+1)-dimensional generalized kadomtsev-petviashvili equation. Eur Phys J Plus. 2019;134(7):371.
Liu X, Triki H, Zhou Q, et al. Analytic study on interactions between periodic solutions with contrltable parameters. nonlinear Dyn. 2018;94(1):703-709.
Yepez-Martinez H, Rezazadeh H, Souleymanou. A, et al. The extended modified method applied to optical solutions in birefringent fibers with weak nonlocal nonlinearity and four wave mixing Chinese J phys. 2019;58:137-150.
Anco SC. Kara AH. Symmetry-invariant conservation laws of partial differential equations. Eur J Appl Math.2018;29(10:78-117.
Bluman GW. Cole JD. Similarity methods for differential equations. New York: Springer;1974.
Bluman GW, Kumei S. Symmetries and differential equations. New York: Springer:1989.
Ozer T. Symmetry group classification for two-dimensional elastodynamics problems in nonlocal elasticity. Int J Eng Sci.2003;41(18):2193-2211.