View source for Popowicz Z. The conserved quantities for the generalized Riemann equation, talk at The Workshop on GDEq and Integrability, 11-15 October 2010, Hradec nad Moravici, Czech Republic (abstract)

{{MeetingTalk
| speaker = Ziemowit Popowicz
| title = The conserved quantities for the generalized Riemann equation
| abstract = We analyze the integrability property of the generalized hydrodynamical Riemann type equation <math>D^N_t u=0</math> for arbitrary <math>N</math>.  The infinite hierarchies of polynomial and non-polynomial conservation laws, both dispersive and dispersionless, are presented. Special attention is paid to the cases <math>N=2</math>, <math>3</math> and <math>N=4</math>, for which the conservation laws, Lax type representations and Hamiltonian structures are analyzed in detail.  We also show that the case <math>N=2</math> 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.
| slides = [[Media:Prikarpatsky_A.K.%2C_Golenia_J.%2C_Artemovych_O.D.%2C_Pavlov_M.%2C_Popowicz_Z._The_conserved_quantities_for_the_generalized_Riemann_equation_%28presentation_at_Workshop_Geom._Diff._Eq._and_Integrability%2C_11-15_October_2010%2C_Hradec_nad_Moravici%2C_Czech_Republic%29.pdf|Prikarpatsky A.K., Golenia J., Artemovych O.D., Pavlov M., Popowicz Z. The conserved quantities for the generalized Riemann equation (presentation at Workshop Geom. Diff. Eq. and Integrability, 11-15 October 2010, Hradec nad Moravici, Czech Republic).pdf]]
| references = Anatoliy K. Prykarpatsky, Orest D. Artemovych, Ziemowit Popowicz, Maxim V. Pavlov Differential-algebraic integrability analysis of the generalized Riemann type and Korteweg-de Vries hydrodynamical equations, J. Phys. A: Math. Theor. '''43''' (2010) 295205, {{arXiv|1005.2660}}

Ziemowit Popowicz, Anatoliy K. Prykarpatsky The non-polynomial conservation laws and integrability analysis of generalized Riemann type hydrodynamical equations, Nonlinearity '''23''' (2010) 2517, {{arXiv|1005.3942}}
| 79YY-MM-DD = 7989-89-85
}}