Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-05-21
Nonlinear Sciences
Exactly Solvable and Integrable Systems
17 pages
Scientific paper
Based on the gradient-holonomic algorithm we analyze the integrability property of the generalized hydrodynamical Riemann type equation $%D_{t}^{N}u=0$ for arbitrary $N\in \mathbb{Z}_{+}.$ The infinite hierarchies of polynomial and non-polynomial conservation laws, both dispersive and dispersionless are constructed. Special attention is paid to the cases $%N=2,3$ and N=4 for which the conservation laws, Lax type representations and bi-Hamiltonian structures are analyzed in detail. We also show that the case N=2 is equivalent to a generalized Hunter-Saxton dynamical system, whose integrability follows from the results obtained. As a byproduct of our analysis we demonstrate a new set of non-polynomial conservation laws for the related Hunter-Saxton equation.
Popowicz Ziemowit
Prykarpatsky Anatoliy K.
No associations
LandOfFree
The non-polynomial conservation laws and integrability analysis of generalized Riemann type hydrodynamical equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The non-polynomial conservation laws and integrability analysis of generalized Riemann type hydrodynamical equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The non-polynomial conservation laws and integrability analysis of generalized Riemann type hydrodynamical equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-339655