TITLE:
Deterministic Chaos of N Stochastic Waves in Two Dimensions
AUTHORS:
Victor A. Miroshnikov
KEYWORDS:
Stochastic Waves, Invariant Structures, Experimental Computation, Theoretical Computation
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.4,
August
29,
2014
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.