Study of Chrip and Chrip-Free Solitons for Distinct Nonlinear Phenomena

Abstract

Solitons are waves that have only one crest. Solitons can therefore travel a considerable distance while preserving their shape. These wave solutions play a vital role in mathemati- cal physics. The particular class of solitons solutions is Korteweg de Varies (KdV) and the nonlinear Schr¨odinger equations (NLSE) .In this thesis, our goal is to acquire variety of solitary wave solutions for two various nonlin- ear models: system of equations of the Atangana Baleanu (AB) fractional derivative for the ion sound and Langmuir waves (ISALWs), Hirota Ramani equation (HRE), PT-symmetric nonlinear directional couplers (NLDC) and Radhakrishnan-Kundu-Laksmannan equation (RKLE). We obtain bright, dark, periodic wave and solitory wave for ISALWs equation. We also retrieve bell type, kink type, singular, Jacbi elliptic function (JEF), Weierstrass- elliptic function (WEF), hyperbolic functions (HF), periodic functions (PF) and other soli- tary wave solutions for HRE using Sub ODE technique under some constraint conditions. At the end we will show our solutions with the help of graphs in distinct dimensions.Key words: Sub-ODE method, Nonlinear models, Fractional calculus.