5,254 research outputs found

### Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation

By performing two parallel numerical experiments -- solving the dynamical
Hamiltonian equations and solving the Hasselmann kinetic equation -- we
examined the applicability of the theory of weak turbulence to the description
of the time evolution of an ensemble of free surface waves (a swell) on deep
water. We observed qualitative coincidence of the results.
To achieve quantitative coincidence, we augmented the kinetic equation by an
empirical dissipation term modelling the strongly nonlinear process of
white-capping. Fitting the two experiments, we determined the dissipation
function due to wave breaking and found that it depends very sharply on the
parameter of nonlinearity (the surface steepness). The onset of white-capping
can be compared to a second-order phase transition. This result corroborates
with experimental observations by Banner, Babanin, Young.Comment: 5 pages, 5 figures, Submitted in Phys. Rev. Letter

### New multidimensional partially integrable generalization of S-integrable N-wave equation

This paper develops a modification of the dressing method based on the
inhomogeneous linear integral equation with integral operator having nonempty
kernel. Method allows one to construct the systems of multidimensional Partial
Differential Equations (PDEs) having the differential polynomial forms in any
dimension n. Associated solution space is not full, although it is parametrized
by a certain number of arbitrary functions of (n-1)-variables. We consider
4-dimensional generalization of the classical (2+1)-dimensional S-integrable
N-wave equation as an example.Comment: 38 page

### Weak Wave Turbulence Scaling Theory for Diffusion and Relative Diffusion in Turbulent Surface Waves

We examine the applicability of the weak wave turbulence theory in explaining
experimental scaling results obtained for the diffusion and relative diffusion
of particles moving on turbulent surface waves. For capillary waves our
theoretical results are shown to be in good agreement with experimental
results, where a distinct crossover in diffusive behavior is observed at the
driving frequency. For gravity waves our results are discussed in the light of
ocean wave studies.Comment: 5 pages; for related work visit http://www.imedea.uib.es/~victo

### Two-dimensional ring-like vortex and multisoliton nonlinear structures at the upper-hybrid resonance

Two-dimensional (2D) equations describing the nonlinear interaction between
upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal
nonlinearity in the equations results in the possibility of existence of stable
2D nonlinear structures. A rigorous proof of the absence of collapse in the
model is given. We have found numerically different types of nonlinear
localized structures such as fundamental solitons, radially symmetric vortices,
nonrotating multisolitons (two-hump solitons, dipoles and quadrupoles), and
rotating multisolitons (azimuthons). By direct numerical simulations we show
that 2D fundamental solitons with negative hamiltonian are stable.Comment: 8 pages, 6 figures, submitted to Phys. Plasma

### Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves

We study the long-time evolution of gravity waves on deep water exited by the
stochastic external force concentrated in moderately small wave numbers. We
numerically implement the primitive Euler equations for the potential flow of
an ideal fluid with free surface written in canonical variables, using
expansion of the Hamiltonian in powers of nonlinearity of up to fourth order
terms.
We show that due to nonlinear interaction processes a stationary energy
spectrum close to $|k| \sim k^{-7/2}$ is formed. The observed spectrum can be
interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of
energy.Comment: 4 pages, 5 figure

### On integration of some classes of $(n+1)$ dimensional nonlinear Partial Differential Equations

The paper represents the method for construction of the families of
particular solutions to some new classes of $(n+1)$ dimensional nonlinear
Partial Differential Equations (PDE). Method is based on the specific link
between algebraic matrix equations and PDE. Admittable solutions depend on
arbitrary functions of $n$ variables.Comment: 6 page

### On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields

It was shown recently that Frobenius reduction of the matrix fields reveals
interesting relations among the nonlinear Partial Differential Equations (PDEs)
integrable by the Inverse Spectral Transform Method ($S$-integrable PDEs),
linearizable by the
Hoph-Cole substitution ($C$-integrable PDEs) and integrable by the method of
characteristics ($Ch$-integrable PDEs). However, only two classes of
$S$-integrable PDEs have been involved: soliton equations like Korteweg-de
Vries, Nonlinear Shr\"odinger, Kadomtsev-Petviashvili and Davey-Stewartson
equations, and GL(N,\CC) Self-dual type PDEs, like Yang-Mills equation. In
this paper we consider the simple five-dimensional nonlinear PDE from another
class of $S$-integrable PDEs, namely, scalar nonlinear PDE which is
commutativity condition of the pair of vector fields. We show its origin from
the (1+1)-dimensional hierarchy of $Ch$-integrable PDEs after certain
composition of Frobenius type and differential reductions imposed on the matrix
fields. Matrix generalization of the above scalar nonlinear PDE will be derived
as well.Comment: 14 pages, 1 figur

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