Hamiltonian structure for two-dimensional extended Green–Naghdi equations

On two-dimensional hamiltonian transport equations

We consider two-dimensional autonomous ows with divergence free continuous coeecients. Under a generic assumption of regularity on the set of critical points, we give a proof of uniqueness for the characteristics and for the transport equation in the framework of distributions.

Constructing Two-Dimensional Multi-Wavelet for Solving Two-Dimensional Fredholm Integral Equations

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

Predicting Two Dimensional Hamiltonian Chaos*

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

Structure and computation of two-dimensional incompressible extended MHD

On the Hamiltonian structure of evolution equations

The theory of evolution equations in Hamiltonian form is developed by use of some differential complexes arising naturally in the formal theory of partial differential equations. The theory of integral invariants is extended to these infinitedimensional systems, providing a natural generalization of the notion of a conservation law. A generalization of Noether's theorem is proved, giving a one-...