Browsing by Author "Hasnain Abbas"

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    Breathers, Rogue Wave and Lump Solutions For Nonlinear Partial Evolution Equation
    (Library Information Services, CUI Lahore, 2022) Hasnain Abbas; CIIT/FA21-RMT-044/LHR
    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 characteris- tic 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 phe- nomena, 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 transforma- tions, 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 ra- tional 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.Key words: Sub-ODE method, nonlinear Schr¨