Recursion operator and dispersionless Lax representation
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We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a dispersionless Lax representation. We consider a polynomial and rational Lax function. We give several examples containing the equations of shallow water waves, polytropic gas dynamics and a degenerate bi-Hamiltonian system with a recursion operator. We also discuss a reduction of N + 1 systems to N systems of some new integrable equations of hydrodynamic type.
Dispersionless Lax Representation
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