Abstract:
Nonlinear evolution equations (NLEEs) play a noteworthy role in various scientific and
engineering fields such as applied mathematics, plasma physics, fluid dynamics, optical fibers,
biology, solid state physics, chemical physics, mechanics and geochemistry. Various effective
procedure have been developed to solve NLEEs. In this work, we have discussed applications of
two types methods: first type is modified double sub-equation (MDSE) method which is apply in
the (1+1)-dimensional Burger equation, the (1+1)-dimensional Gardner equation and the (1+1)-
dimensional Hirota-Ramani equation and secondly, Hirota’s Bilinear method which is apply in
(2+1)-dimensional Breaking Soliton, the (2+1)-dimensional asymmetric Nizhnik-Novikov-
Veselov equations, and (3+1)-D generalized B-type Kadomtsev-Petviashvili equation.
Using Modified double sub-equation method, we have presented some complexiton solutions in
terms of trigonometric, hyperbolic functions. Finally, the interaction phenomena of the achieved
complexiton solutions between solitary waves and/or periodic waves are presented with in depth
derivation.
Based on the bilinear formalism and with the aid of symbolic computation, we determine multisolitons,
breather solutions, rogue wave, lump soliton, lump-kink waves and multi lumps using
various ansatze’s function. We notice that multi-lumps in the form of breathers visualize as a
straight line. Besides this, the breather wave degenerate into a single lump wave is determined by
using parametric limit scheme. Also, we reflect a new interaction solution among lump, kink and
periodic waves via ‘rational-cosh-cos’ type test function. To realize dynamics, we commit diverse
graphical analysis on the presented solutions. Obtained solutions are reliable in the mathematical
physics and engineering.----
Description:
This Thesis is Submitted to the Department of Mathematics , University of Rajshahi, Rajshahi, Bangladesh for The Degree of Master of Philosophy (MPhil)
