A new method of studying the dynamical behaviour of the sine-Gordon equation. (English) Zbl 1020.35523
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35L70 | Second-order nonlinear hyperbolic equations |
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
References:
| [1] | Bishop, A. R.; Flesch, R. F., SIAM J. Math. Anal., 21, 1511 (1990) |
| [2] | Temam, R., Infinite dimensional dynamical systems in mechanics and physics (1988), Springer: Springer Berlin · Zbl 0662.35001 |
| [3] | Constantin, P.; Foias, C.; Nicolaenko, B.; Temam, R., Integral manifolds and inertial manifolds for dissipative partial differential equations (1988), Springer: Springer Berlin · Zbl 0683.58002 |
| [4] | Cross, M. C.; Hohenberg, P. C., Rev. Mod. Phys., 65, 851 (1993) · Zbl 1371.37001 |
| [5] | Zengrong, Liu; Zhenyuan, Xu; Weiming, Xie, Adv. Mech., 21, 421 (1991) · Zbl 0748.58016 |
| [6] | Zengrong, Liu; Zhenyuan, Xu; Guoping, Ling; Guanxiang, Wang, discussion of the dynamical behaviour of the sine-Gordon equation, Nonlin. Dyn. (1995), to be published |
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