On the numerical solution of the sine-Gordon equation

Journal Article · Sat Mar 01 04:00:00 EST 1997 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1996.5606· OSTI ID:494298

Ablowitz, M J ^[1]; Herbst, B M ^[2]; Schober, C M ^[3]

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1. Univ. of Colorado, Boulder, CO (United States)
2. Univ. of Cape Town, Rondebosch (South Africa)
3. Old Dominion Univ., Norfolk, VA (United States)

The phase space of sine-Gordon possesses tori and homoclinic structures. It is important to determine how these structures are preserved by numerical schemes. In this, the second of two papers on the numerical solution of the sine-Gordon equation, we use the nonlinear spectrum as a basis for comparing the effectiveness of symplectic and nonsymplectic integrators in capturing infinite dimensional phase space dynamics. In particular, we examine how the preservation of the nonlinear spectrum (i.e., the integrable structure) depends on the order of the accuracy and the symplectic property of the numerical scheme. 19 refs., 20 figs., 1 tab.

• OSTI ID: 494298
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 131; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
HAMILTONIANS
NUMERICAL SOLUTION
PHASE SPACE
RUNGE-KUTTA METHOD
SINE-GORDON EQUATION