Numerical analysis of Non-Linear Waves Propagation and interactions in Plasma

Abstract

Solitary wave propagation and interaction in plasma using numerical tools like Galerkin Finite Element scheme are discussed in this paper. A one-dimensional nonlinear Schrodinger-Korteweg De-Vries (Sch-KdV) equation is taken as model equation for Non-linear waves propagation in the said media. The derived system, with the help of cubic B-spline source functions are engaged as element and weight functions, after finite element formulation is solved with Runge Kutta Fourth Order method (RK4 ). Previously the finite element methods with some numerical simulations do not exhibit the complex nature of wave interaction, especially solitary wave interaction. A combination of Galerkin Finite Element scheme with RK4 is a very prominent instrument to study the nature of Non-linear evolution equations in ionic medias, which is the novelty of the paper.