scholarly journals V ect(S1) Action on Pseudodifferential Symbols onS1and (Noncommutative) Hydrodynamic Type Systems

2006 ◽  
Vol 13 (4) ◽  
pp. 549-565 ◽  
Author(s):  
Partha Guha
Keyword(s):  
Type Systems ◽  
Hydrodynamic Type

scholarly journals Symmetry group analysis and invariant solutions of hydrodynamic-type systems

2004 ◽  
Vol 2004 (10) ◽  
pp. 487-534 ◽  
Author(s):  
M. B. Sheftel
Keyword(s):  
Group Analysis ◽  
Type Systems ◽  
Hydrodynamic Type ◽  
Recursion Operators ◽  
Higher Symmetries ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Component Systems ◽  
Two Component Systems ◽  
Existence Conditions

We study point and higher symmetries of systems of the hydrodynamic type with and without an explicit dependence ont,x. We consider such systems which satisfy the existence conditions for an infinite-dimensional group of hydrodynamic symmetries which implies linearizing transformations for these systems. Under additional restrictions on the systems, we obtain recursion operators for symmetries and use them to construct infinite discrete sets of exact solutions of the studied equations. We find the interrelation between higher symmetries and recursion operators. Two-component systems are studied in more detail thann-component systems. As a special case, we consider Hamiltonian and semi-Hamiltonian systems of Tsarëv.

Hamiltonian dynamics of vortex lines in hydrodynamic-type systems

JETP Letters ◽  
1998 ◽  
Vol 67 (12) ◽  
pp. 1076-1081 ◽  
Author(s):  
E. A. Kuznetsov ◽  
V. P. Ruban
Keyword(s):  
Hamiltonian Dynamics ◽  
Type Systems ◽  
Hydrodynamic Type ◽  
Vortex Lines
Sign in / Sign up

Export Citation Format

Share Document