Abstract:
Solitons demonstrate an explanatory role in a multitude of physical phenomena in the
scientific domain of the world. Owing to the non-availability of exact solutions in many
non-linear physical problems, various analytical and non-analytical schemes have
evolved. This study is concerned with the establishment of analytical solutions for
nonlinear partial differential equations. With the evolution of time, the flourishing part
of the fundamental phenomenon of soliton has gained considerable utility and the
attention of researcher and scientists. Solitons are a special kind of nonlinear waves
that are able to maintain their shape along with the promulgation. Few related
problems have been discussed and resolved using Exp-Function Methods. The specific
narrative aims to contribute an instinctive grasp for Exp-Function Method, Modified
Exp-Function
Exp
method,
Exp
))-Expansion
Method
and
Novel
Rational
))-Expansion Method. Moreover, these methods introduce several types of
the solutions like hyperbolic, trigonometric and rational solutions. Likewise, we shall
protract novel expansion method for the problems occurring in mathematical physics of
varied differential equations. The proposed methods are capable of determining
nonlinear differential equations, their systems and several differential equations of
fractional order. The Multiple Exp-function Method has been employed as N-soliton
solution to different problems, which further elaborates the efficacy and accuracy of the
proposed algorithm.
