Abstract:
Nonlinear Partial Differential Equations (NLPDEs) are commonly used as models to iden-
tify several kinds of physical phenomena and play an important role in multiple fields.A
soliton is a localised, single wave that has a consistent shape. Solitons represent a balance
of dispersion and nonlinear effects. It is common to interchange the terms lonely wave and
solitary on. Both continuous and discrete systems exhibit lone waves. They are also known
as shallow-water waves having a specific shape. When a soliton collides with another one,
it retains its original shape. John Scott Russell made the first solitary wave observation in
1934. This hump-shaped confined wave propagates in a single spatial direction and exhibits
exceptional stability characteristics. He had the idea for wave translation. Russell discov-
ered the velocity of a single wave. Solitons are basically solitary wave solutions. There
are two categories of solitons bright and dark. Our goal in this thesis is to obtain multi-
ple soliton solutions for various types of NLPDEs by using the generalised Kudryashov
method (GKM) and the Sine-Cosine method (SCM), respectively. We will study various
type of NLPDEs like The Jaulent-Miodek hierarchy (JMh) and Calogero Bogoyavlenskii
Schiff (CBS) with the help of above mentioned techniques. We will obtain bright solitons
and dark solitons.
