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The wavelet transform method originated by Wei et al. [Phys. Rev. Lett. 89, 284103.4 (2002)] was proved [Juang and Li, J. Math. Phys. 47, 072704.16 (2006); Juang et al., J. Math. Phys. 47, 122702.11 (2006); Shieh et al., J. Math. Phys. 47, 082701.10 (2006)] to be an effective tool to reduce the order of coupling strength for coupled chaotic systems to acquire the synchrony regardless the size of oscillators. In Juang et al., [IEEE Trans. Circuits Syst., I: Regul. Pap. 56, 840 (2009)] such method was applied to coupled map lattices (CMLs). It was demonstrated that by adjusting the wavelet constant of the method can greatly increase the applicable range of coupling strengths, the parameters, range of the individual oscillator, and the number of nodes for local synchronization of CMLs. No analytical proof is given there. In this paper, the optimal or near optimal wavelet constant can be explicitly identified. As a result, the above described scenario can be rigorously verified. [ABSTRACT FROM AUTHOR]

In this paper, we numerically investigate the dynamics of the solitary waves in the presence of damping and external stochastic forces for the improved Boussinesq equation. The hydrodynamical and Stokes damping will be considered respectively. Since the analytic solutions for the considered problems are not available, Monte Carlo method will be used in random space and finite volume element method will be used in physical space. Numerical results demonstrate that solitary wave profile is not strongly affected by the Gaussian white noise in our study. The average of the velocity of the solitary waves is very close to that for the deterministic case. [ABSTRACT FROM AUTHOR]