Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-07-22
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Latex, 34 pages
Scientific paper
Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the integrability of such systems by the generalised hodograph transform implies that integrable Hamiltonians depend on a certain number of arbitrary functions of two variables. On the contrary, in 2+1 dimensions the requirement of the integrability by the method of hydrodynamic reductions, which is a natural analogue of the generalised hodograph transform in higher dimensions, leads to finite-dimensional moduli spaces of integrable Hamiltonians. In this paper we classify integrable two-component Hamiltonian systems of hydrodynamic type for all existing classes of differential-geometric Poisson brackets in 2D, establishing a parametrisation of integrable Hamiltonians via elliptic/hypergeometric functions. Our approach is based on the Godunov-type representation of Hamiltonian systems, and utilises a novel construction of Godunov's systems in terms of generalised hypergeometric functions.
Ferapontov E. V.
Odesskii A. V.
Stoilov M. N.
No associations
LandOfFree
Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-610605