Chirped Optical and Solitary Waves for Different Forms of NLSEs

Abstract

Chirped Optical and Solitary Waves for Different Forms of NLSEs The solitary waves (SW) are represented by the solutions of the nonlinear integrable partial differential equation (NLPDE). Solitons, also known as SW, have a very interesting back ground. On the surface of the water, Russell made the very first scientific observation of solitons in the year 1834. The Korteweg-deVries equation is an example of a NLPDE that can be solved to provide soliton solutions. Equations such as the Sinh-Gordon (SG) equa tion, the Kadomtsev-Petviashvili (KP) equation, and the resonant nonlinear Schrodinger ¨ equation (NLSE), amongst others, have been developed. Solitons can be seen in a wide variety of nonlinear phenomena, including fluid dynamics, plasma physics, biological and atmospheric systems, nonlinear fibre optics and many more. Solitons are the result of a trade-off between nonlinearity and dispersion. The investigation of soliton pulse solutions with nonlinear chirping has proven to be an intriguing subject of study. Chirped solitons are a relatively new solitary wave phenomenon. Chirp is a frequency utilised in spread spectrum communications as well as various sonar and radar systems. In this thesis, we will first obtain various chirped periodic and solitons waves by employ ing the Jacobian elliptic function (JEF) for the coupled NLSE with competing weakly non local and parabolic law nonlinearities (CWN-PLNL) and a generalized mixed nonlinear Schrodinger (GMNLS) equation model. We also obtain some solitary waves (SW) solu- ¨ tions for the governing model, such as bright, dark, hyperbolic, kink, periodic, and others. Also determined is the chirp that corresponds to each of these optical solitons. In addition, we will show graphical representations of our solutions in various dimensions.