Solitons Of Bilinear KdV Equation And High Dispersive Schr?dinger Equation

Partial differential equation is a reflection of the restricting relation between the time derivatives and the spatial derivatives of the unknown variables.It models various physical phenomena and plays a significant role in many applications,such as acoustics,fluid dynamics,electrodynamics,heat transfer,nonlinear optics and photonics,as well as the dynamics of light pulses.Thus,constructing exact solutions for such meaningful partial differential equations is an important task in nonlinear sciences.For this propose,many mathematical tools have been employed to find traveling wave solutions,such as the B?cklund transformation,Hirota bilinear method and various function expansion methods.In this paper,with the help of the Jacobi elliptic function method,Ansatz method and complete discrimination system,we have derived a plenty of new solutions for two types of partial differential equations.In Section 1,we introduce the background information about these two partial differential equations.In Section 2,we use the Jacobi elliptic function expansion method,Ansatz method to derive the traveling wave solutions of the bilinear KdV equation,which consists of solitary patterns solutions,periodic solutions and Jacobi elliptic functions solutions under different conditions.In Section 3,the complete discrimination system is employed to find exact solutions for the high dispersive Schr?dinger equation.As a result,we derive a range of solutions which includes triangular function solutions,kink solitary wave solutions,dark solitary wave solutions,Jacobian elliptic function solutions,rational function solutions and implicit analytical solutions.