On the Numerical Solution of the Sine–Gordon Equation

✍ Scribed by M.J. Ablowitz; B.M. Herbst; C.M. Schober

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 588 KB
• Volume: 131
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.5606

✦ Synopsis

detail why the symplectic property is so important for planar Hamiltonian systems. The question is whether this

The phase space of sine-Gordon possesses tori and homoclinic structures. It is important to determine how these structures are superior behavior carries over to high-dimensional syspreserved by numerical schemes. In this, the second of two papers tems, as our earlier experiments with symplectic inteon the numerical solution of the sine-Gordon equation, we use the grators of the sine-Gordon equation might indicate. In nonlinear spectrum as a basis for comparing the effectiveness of this paper we set out to answer this question.

symplectic and nonsymplectic integrators in capturing infinite di-

In order to determine the effectiveness of symplectic mensional phase space dynamics. In particular, we examine how the preservation of the nonlinear spectrum (i.e., the integrable structure) integrators, it is very useful to have a simple description depends on the order of the accuracy and the symplectic property of the geometry of phase space which can be used to deterof the numerical scheme. ᮊ 1997 Academic Press mine how well the numerical schemes preserve the phase space structure. Fortunately, such a description based upon the spectrum of the associated linear eigenvalue problem