Exact Soliton of Fifth Order (1+1) Dimensional Triple Non-Linear Partial Differential Equations on Modified Truncated Expansion Methods

Abstract

In this manuscript, modified truncated expansion method-I taking the traveling wave variable $u(x, t)=y(r)=y(kx+wt)$ and modified truncated expansion method-II introducing the traveling wave variable $u(x, t) = y(r)=y(kx − wt)$ are built up to obtain analytical solution in the form of traveling wave solutions with different frequencies and velocities that can be constructed for triple (1+1) dimensional nonlinear partial differential equations (NLPDEs) such as Sawada-Kotera equation (SKE), generalized Korteweg-de Vries equation (GKdVE) and Kaup-Kuperschmidt equation (KKE), which have been widely used in mathematical physics. The present topic minimizes the complex nature and non-integrable characteristics to obtain solutions of NLPDEs. To demonstrate the influence of the parameters, 3D plots are generated for triple NLPDEs. This content is employed in physics such as magneto sound in plasma and nonlinear optics.