Numerical solutions of the coupled nonlinear Klein--Gordon equations by   trigonometric integrator pseudospectral discretization
  A scheme stemming from the use of pseudospectral approximations to spatial derivatives followed by a time integrator based on trigonometric polynomials is proposed for the numerical solutions of the coupled nonlinear Klein--Gordon equations. Numerical tests on one- and three-coupled Klein--Gordon equations are presented, which are geared towards understanding the accuracy and stability, and demonstrating the efficiency and high resolution capacity in application. 
Xuanchun Dong
math-ph math.MP