Time-space Jacobi pseudospectral simulation of multidimensional
Schrodinger equation
Abstract
In this paper, the authors investigate the interaction of soliton waves
for multidimensional nonlinear Schrodinger equation (NSE) using
time-space Jacobi pseudospectral method. The proposed method is
established in both time and space to approximate the solutions and to
prove the stability analysis for the equations. Using the Jacobi
derivatives matrices the given problem is reduced to a system of
nonlinear algebraic equations, which will be solved using Newton’s
Raphson method. For numerical experiments, the method is tested on a
number of different examples to study the behavior of interaction of two
and more than two soliton, single soliton. Moreover, numerical solutions
are demonstrated to justify the theoretical results and confirm the
expected convergence rate. Comparison of numerical and exact solution is
depicted in the form of figures and tables.