Hydrodynamic Diffusion in Integrable Systems

Differential Geometry of Strongly Integrable Systems of Hydrodynamic Type

Here the matrix (gij) (assumed nondegenerate) defines a pseudo-Riemannian metric (with upper indices) of zero curvature on the u-space, Fjk i = Fjki(u) being the corresponding Levi-Civita connection. Thus, the integrability condition can be formulated in terms of the differential geometry of SHT. For such integrable systems S. P. Tsarev [3] found a generalization (for N _> 3) of the hodograph m...

Transformations of integrable hydrodynamic chains and their hydrodynamic reductions

Hydrodynamic reductions of the hydrodynamic chain associated with dispersionless limit of 2+1 Harry Dym equation are found by the Miura type and reciprocal transformations applied to the Benney hydrodynamic chain.

Arnold diffusion in perturbations of analytic integrable Hamiltonian systems

Algebro-geometric approach in the theory of integrable hydrodynamic type systems

The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. This method is significantly simplified for so-called symmetric hydrodynamic type systems. Plenty interesting and physically motivated examples are investigated.

Integrable Boundary Conditions in Asymmetric Diffusion Processes

We study non-equilibrium reaction-diffusion processes with open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be determined in an elementary way. We give the equation which includes an auxiliary parameter and determines possible boundary conditions for the model to be solved exactly...