Short-Time Existence for Scale-Invariant Hamiltonian Waves
نویسنده
چکیده
We prove short-time existence of smooth solutions for a class of nonlinear, and generally spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations include ones that describe weakly nonlinear hyperbolic surface waves, such as nonlinear Rayleigh waves in elasticity.
منابع مشابه
Invariant Tori in Hamiltonian Systems with High Order Proper Degeneracy
We study the existence of quasi-periodic, invariant tori in a nearly integrable Hamiltonian system of high order proper degeneracy, i.e., the integrable part of the Hamiltonian involves several time scales and at each time scale the corresponding Hamiltonian depends on only part of the action variables. Such a Hamiltonian system arises frequently in problems of celestial mechanics, for instance...
متن کاملNumerische Simulation Auf Massiv Parallelen Rechnern Preprint-reihe Des Chemnitzer Sfb 393 Lagrangian Invariant Subspaces of Hamiltonian Matrices
The existence and uniqueness of Lagrangian invariant subspaces of Hamiltonian matrices is studied. Necessary and suucient conditions are given in terms of the Jor-dan structure and certain sign characteristics that give uniqueness of these subspaces even in the presence of purely imaginary eigenvalues. These results are applied to obtain in special cases existence and uniqueness results for Her...
متن کامل0 50 50 50 v 1 1 9 M ay 2 00 5 Scale Invariant Spectra of the Oceanic Internal Wave Field
We present a theory predicting the high-frequency-high-wavenumber part of the spectral energy density of internal waves in the ocean. The theory is based on the wave turbulence formalism applied to a natural Hamiltonian description for the internal wave field. We show that stationary energy spectra form a family of statistically steady state scale invariant solutions. Remarkably, the high-frequ...
متن کاملIntroduction to Schramm-Loewner evolution and its application to critical systems
In this short review we look at recent advances in Schramm-Loewner Evolution (SLE) theory and its application to critical phenomena. The application of SLE goes beyond critical systems to other time dependent, scale invariant phenomena such as turbulence, sand-piles and watersheds. Through the use of SLE, the evolution of conformally invariant paths on the complex plane can be followed; hence a...
متن کاملOn a Hamiltonian PDE arising in Magma Dynamics
In this article we discuss a new Hamiltonian PDE arising from a class of equations appearing in the study of magma, partially molten rock, in the Earth’s interior. Under physically justifiable simplifications, a scalar, nonlinear, degenerate, dispersive wave equation may be derived to describe the evolution of φ, the fraction of molten rock by volume, in the Earth. These equations have two powe...
متن کامل