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arXiv · 0912.4954

Classification of conservative hydrodynamic chains. Vlasov type kinetic equation, Riemann mapping and the method of symmetric hydrodynamic reductions

Maxim V. Pavlov·Sergej A. Zykov
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Abstract

A complete classification of integrable conservative hydrodynamic chains is presented. These hydrodynamic chains are written via special coordinates -- moments, such that right hand sides of these infinite component systems depend linearly on a discrete independent variable $k$. All variable coefficients of these hydrodynamic chains can be expressed via modular forms with respect to moment $A^{0}$, via hypergeometric functions with respect to moment $A^{1}$; they depend polynomially on moment $A^{2}$ and linearly on all other higher moments $A^{k}$. A dispersionless Lax representation is found. Corresponding collisionless Boltzmann (Vlasov like kinetic) equation is derived. A Riemann mapping is constructed. A generating function of conservation laws and commuting flows is presented.

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Maxim V. Pavlov, Sergej A. Zykov. 2009-12-25. Classification of conservative hydrodynamic chains. Vlasov type kinetic equation, Riemann mapping and the method of symmetric hydrodynamic reductions. https://arxiv.org/abs/0912.4954

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