TITLE:
Nonlinear Interaction of N Conservative Waves in Two Dimensions
AUTHORS:
Victor A. Miroshnikov
KEYWORDS:
Structures, Waves, Computation, Experiment, Theory
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.3,
May
16,
2014
ABSTRACT:
Kinematic Fourier
(KF) structures, exponential kinematic Fourier (KEF) structures, dynamic
exponential (DEF) Fourier structures, and KEF-DEF structures with constant and
space-dependent structural coefficients are developed in the current paper to
treat kinematic and dynamic problems for nonlinear interaction of N conservative waves in the
two-dimensional theory of the Newtonian flows with harmonic velocity. The
computational method of solving partial differential equations (PDEs) by
decomposition in invariant structures, which continues the analytical methods
of undetermined coefficients and separation of variables, is extended by using
an experimental and theoretical computation in Maple?. For internal waves
vanishing at infinity, the Dirichlet problem is formulated for kinematic and
dynamics systems of the vorticity, continuity, Helmholtz, Lamb-Helmholtz, and
Bernoulli equations in the upper and lower domains. Exact solutions for upper and
lower cumulative flows are discovered by the experimental computing, proved by
the theoretical computing, and verified by the system of Navier-Stokes PDEs.
The KEF and KEF-DEF structures of the cumulative flows are visualized by
instantaneous surface plots with isocurves. Modeling of a deterministic wave
chaos by aperiodic flows in the KEF, DEF, and KEF-DEF structures with 5N parameters is considered.