Study of Breathers and M-Shaped Solutions to Nonlinear Models

Abstract

A soliton is a localised solitary wave with a constant structure that recovers its shape after col- lision. We obtain a soliton solution as a result of the balance dispersion and nonlinear effects. Solitons are generated in a variety of material and have several applications. Solitons have a broad range of applications, which suggests that they frequently occur in a variety of physics domains.In this thesis, exponential, hyperbolic and trigonometric function will be combined to analyse various NLEEs to get some solutions. Our goal in this work is to find rogue soliton wave solu- tion (RSW), lump soliton wave solution (LSW), lump with one (LSW1K) and two kink soliton wave solution (LSW2K), periodic soliton waves solution (PSW), correspondence between lump kink and periodic soliton wave (LPKSW) for different types of NLEEs. Additionally, M type interaction with periodic and kink soliton waves solution (MSPKSW), M type correspondence with rogue and kink soliton waves solution (MSRKSW), M type rational soliton wave solution (MSRSW), M type rational interaction with one kink wave (MSR1K) and two kink (MSR2K), periodic cross rational soliton wave solution (PCRSW), kink cross rational soliton wave solu- tion (KCRSW), periodic cross kink soliton wave solution (PCKSW), periodic cross lump soli- ton wave solution (PCLSW), breather soliton wave (BSW), homoclinic breather soliton wave solution (HBSW) and multiwave soliton wave solutions (MWSW) will be obtained. We also observed the degeneration of waves through bilinear form and also reviewed the graphical be- haviour of our solutions for quadratic nonlinearity (QN) model and cold bosonic atoms in a zig zag optical lattice (CBAZZ) model.