Various Forms Of Lump Solutions For Nonlinear

Abstract

Soliton is a certain kind of wave which propagate with constant speed and form, another prop- erty is that solitons continue their speed and shape after collisions with other solitons. Solitons can be obtained in a diversity of materials and are used for various purposes. There are various forms of soliton one of renowned form is lump soliton. Lump wave are rationally localized in all directions. Lump solutions appear in various areas of sciences like atmosphere, capillary flow, plasma, oceanographic engineering. Another very renowned wave phenomenon is rogue waves also known as killer or monster waves appear mostly in ocean. Rogue wave are spe- cial type of rational solutions. M-shape rational solutions are another sort of soliton. It is also known as combined solitary waves (CSW). CSW is used to create dark and bright solitons in communication systems and femtosecond laser systems. Breather solitons are another type of soliton. Breather is a nonlinear wave that oscillates in time but does not spread in space. In this work, our purpose is to obtain rogue–waves, periodic–waves, lump, lump with one and two-kink solitons solution for various forms of NLPDEs. We’ll achieved M-shaped rational so- lutions, rogue waves, multi-wave, periodic-cross lump, homoclinic breather approach, periodic cross-kink, lump with one and two kink, M-shaped interaction with kink and rogue wave, and periodic solutions for nonlinear Atangana conformable Boussinesq-like equations (NLACBEs). In Chapter III, we’ll study various analytical solutions like periodic cross–kink wave (PCKW), rogue waves solutions, periodic solution, lump with two kink of (2+1)-dimensional space time fractional Bogoyavlenskii equation and also observed graphical behavior of our system