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Conservation laws of the generalized Riemann equations. (English) Zbl 1420.35158

Summary: Two special classes of conserved densities involving arbitrary smooth functions are explicitly formulated for the generalized Riemann equation at arbitrary \(N\). The particular case when \(N=2\) covers most of the known conserved densities of the equation, and the result is also extended to the famous Gurevich-Zybin, Monge-Ampere and two-component Hunter-Saxton equations by considering certain reductions.

MSC:

35L65 Hyperbolic conservation laws
35L60 First-order nonlinear hyperbolic equations
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
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References:

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