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Numerical analysis of long-time dynamic behavior in weakly damped forced KdV equation. (English) Zbl 1003.76069

Summary: We describe numerical analysis of approximate inertial manifold in weakly damped forced KdV equation. The results of numerical analysis for five models are the same as those of nonlinear spectral analysis.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76B25 Solitary waves for incompressible inviscid fluids
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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References:

[1] Temam R.Infinite Dimensional Systems in Mechanics and Physics [M]. Berlin: Springer-Verlag, 1988. · Zbl 0662.35001
[2] Constantin P, Foias C, Nicolaenko B, et al.Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations [M]. Berlin: Springer-Verlag, 1988. · Zbl 0683.58002
[3] Cross M C, Hohenberg P C. Pattern formation of equilibrium [J].Rev. Modern Phys, 1993,65(2): 851–1223. · Zbl 1371.37001 · doi:10.1103/RevModPhys.65.851
[4] TIAN Li-xin, XU Zhen-yuan. The research of longtime dynamics behavior in weakly damped KdV equation [J].Applied Mathematics and Mechanics (English Edition), 1997,18(10): 1021–1028. · Zbl 0904.35082
[5] Ercolani N M, Mclaughin D W, Roitner H. Attractors and transients for a perturbed periodic KdV equations: a nonlinear spectral analysis [J].Nonlinear Science, 1993,3(2): 477–579. · Zbl 0797.35145 · doi:10.1007/BF02429875
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