Abstract:
Solitons are wave packets or pulses that exhibit exceptional behavior by preserving their
shape and speed while traveling through a medium. Their remarkable stability sets them
apart from typical wave phenomena, as they resist dispersion and retain their characteristic
features intact. Solitons emerged as a concept within fluid dynamics during the 19th
century, and their discovery is attributed to John Scott Russell, a Scottish engineer and
scientist.
In this thesis, our objective is to investigate and achieve various wave patterns and phenomena,
including lump solitons (LS), lump 1 stripe soliton interaction solutions, lump
2 stripe soliton interaction solutions, generalized breathers(GBs), rogue waves (RW), first
order soliton solution, Y-type bifurcation soliton and second order solution, interactions
between lump periodic and kink waves, periodic cross kink waves (PCKW), lumps with
one kink (L1K), lumps with two kinks (L2K), periodic cross lump waves, periodic waves
(PW), and multi waves (MW). To analyze these patterns, we employ ansatz transformations,
which allow us to explore homoclinic breathers (HB), kink cross rational solutions
(KCRS), periodic cross rational solutions (PCRS), M-shaped rational solutions (MSRS),
M-shaped interactions with rogue and kink waves, M-shaped interactions with periodic
and kink waves, M-shaped rational solutions with one kink (MSRS 1k), and M-shaped rational
solutions with two kinks (MSRS 2k). Additionally, we study the dynamic behavior
of our obtained solutions through the utilization of 3D, 2D, and contour plots.
