Study of Chirp Solitons and Rogue Wave Solutions

Abstract

Nonlinear Evolution Equations (NLEEs) are a type of mathematical equation, commonly a partial differential equation (PDE), that describe the evolution of physical phenomena with nonlinear behaviours across time. These equations are critical in many scientific disciplines, including mathematical modelling and soliton theory. The solutions of the NLEEs represent the solitary waves (SW) called solitons. The solitary waves or solitons have a very unique history.Solitons are observed as a dispersion and nonlinearity balance. They are common in many different sectors and have intriguing qualities that make them useful in a variety of applications. The chirped solitons are a recently popular solitary wave phenomenon. Chirp is used in spread spectrum communications as well as some sonar and radar devices. In this thesis, firstly we will obtain some chirped periodic and solitons wave by using Jacobian elliptic function (JEF) for for higher order NLSE with anomalous dispersion regime. We also obtain some solitary waves (SW) like dark, bright, kink, hyperbolic, periodic and other solutions for the governing model. The chirp that corresponds to each of these optical solitons is also determined. We will also display the graph of our solutions in different dimensions. Secondly we will study different analytical solutions for Susceptible-Infectious- Recovered (SIR) epidemic model with specific nonlinear incidence rate and spatial diffusion like lump waves (LW), rogue waves (RW), periodic wave (PW) and periodic-cross lump waves (PCLW). This model offers useful information for containment methods by simulating and understanding the geographical spread of infectious illnesses. It advances our knowledge of how the dynamics of an epidemic are influenced by the movement of infected and susceptible people across space.