Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2009-12-25
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
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.
Pavlov Maxim V.
Zykov Sergej A.
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