NUMERICAL SIMULATION OF QUASI-PERIODIC SOLUTIONS OF THE SINE-GORDON EQUATION

摘要

Analytic solutions of the sine-Gordon equation corresponding to periodic boundary conditions can be complicated, especially if initial values are chosen in the vicinity of homoclinic orbits. For such initial values it has been demonstrated that numerical solutions develop instabilities and may become chaotic. Because of the analytical complexities one cannot easily calculate the accuracy of the numerical solutions and therefore compare different numerical schemes in a straightforward manner. In this note we evaluate numerical methods in terms of the nonlinear spectrum. In particular, it provides one with a means of comparing symplectic and nonsymplectic integrators for integrable infinite dimensional Hamiltonian systems. [References: 11]