Deterministic Chaos of N Stochastic Waves in Two Dimensions

Victor A. Miroshnikov

Department of Mathematics, College of Mount Saint Vincent, New York, USA.

DOI: 10.4236/ajcm.2014.44025                

Abstract

Kinematic exponential Fourier (KEF) structures, dynamic exponential (DEF) Fourier structures, and KEF-DEF structures with time-dependent structural coefficients are developed to examine kinematic and dynamic problems for a deterministic chaos of N stochastic waves in the two-dimensional theory of the Newtonian flows with harmonic velocity. The Dirichlet problems are formulated for kinematic and dynamics systems of the vorticity, continuity, Helmholtz, Lamb-Helmholtz, and Bernoulli equations in the upper and lower domains for stochastic waves vanishing at infinity. Development of the novel method of solving partial differential equations through decomposition in invariant structures is resumed by using experimental and theoretical computation in Maple?. This computational method generalizes the analytical methods of separation of variables and undetermined coefficients. Exact solutions for the deterministic chaos of upper and lower cumulative flows are revealed by experimental computing, proved by theoretical computing, and justified by the system of Navier-Stokes PDEs. Various scenarios of a developed wave chaos are modeled by 3N parameters and 2N boundary functions, which exhibit stochastic behavior.

Keywords

Stochastic Waves, Invariant Structures, Experimental Computation, Theoretical Computation

Conflicts of Interest

The authors declare no conflicts of interest.

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