Numerical And Exact Solutions For Various Nonlinear

Abstract

A soliton is a particular type of solitary wave, that is retrieved as a result of integrable NLPDE. There are different type of solutions like analytic and approximate solutions exist. An exact solution is a symbolic representation of a value which solves a given equation exactly, while a numerical solution is numerical representation of a value which solves a given equation exactly or approximately. Numerical solutions are very usefull when we are unable to retrieve analytic solution. It is also used for comparison with analytic solutions. A lot of analytic and numer- ical methods exists in literature to solve the NLPDEs such as Bernouli’s equation approach, extended tanh method, modified simple equation method and RK methods etc. In this work, our purpose is to attain bell-type, kink and anti kink type, singular solitons and power series solutions for various forms of NLEEs. We’ll also obtain Weierstrass elliptic func- tions, Jacobi elliptic functions in terms of hyperbolic, trigonometric and rational functions. In this thesis, we’ll study various forms of NLEEs to attained these types of solutions with the help of various method like sine-cosine method (SCM), csch method, tan-cot method, sub-ode technique and residual power series method (RPSM). We will also compare our exact solutions with numerical solutions and then represent these solutions graphically.