An Effective Algorithm for Finding Multidimensional Conservation Laws for Integrable Systems of Hydrodynamic Type

2018 ◽  
Vol 194 (2) ◽  
pp. 274-283 ◽  
Author(s):  
Z. V. Makridin
Keyword(s):  
Conservation Laws ◽  
Integrable Systems ◽  
Hydrodynamic Type ◽  
Effective Algorithm ◽  
Systems Of Hydrodynamic Type

scholarly journals New cosmological solutions in hybrid metric-Palatini gravity from dynamical symmetries

2021 ◽  
pp. 2150100
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Conservation Laws ◽  
Integrable Systems ◽  
Functional Form ◽  
Analytic Solutions ◽  
Momentum Conservation ◽  
Field Equations ◽  
Dynamical Symmetries ◽  
Cosmological Solutions ◽  
Liouville Integrable

We investigate the existence of Liouville integrable cosmological models in hybrid metric-Palatini theory. Specifically, we use the symmetry conditions for the existence of quadratic in the momentum conservation laws for the field equations as constraint conditions for the determination of the unknown functional form of the theory. The exact and analytic solutions of the integrable systems found in this study are presented in terms of quadratics and Laurent expansions.

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