Asymptotic Evaluation Methods of Nonlinear Differential Equations Near the Instability Point
The purpose of this paper is to present a general method [Suzuki, 1976a, b, 1977a, b, c, 1978, 1980, in press, to be published] to evaluate asymptotically solutions of nonlinear stochastic differential equations or Langevin’s equations when the system is initially located at or near the unstable point. One of our keypoints is to notice the existence of the scaling regime in an intermediate time region, in which the temporal evolution of physical quantities is expressed by a certain scaling function of the so-called scaling variable τ = S(t, ɛ, …) of time t and the relevant smallness parameter ɛ. Namely, we divide the whole time region into three regimes, i.e., initial, second (scaling), and final regimes.
KeywordsNonlinear Differential Equation Nonlinear Transformation Transient Phenomenon Instability Point Final Regime
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- Suzuki, M., in press, in: “Proceedings of the XVII Solvay Conference on Physics”, John Wiley and Sons, Inc., N.Y. Suzuki, M., to be published, in: “Lecture Notes in Physics. Proceedings of the Vlth Sites Conference on Statistical Mechanics”, Springer-Verlag, Berlin.Google Scholar