On a Nonlocal Ostrovsky-Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability

被引:19
作者
Golenia, Jolanta [1 ]
Pavlov, Maxim V. [2 ]
Popowicz, Ziemowit [3 ]
Prykarpatsky, Anatoliy K. [4 ,5 ]
机构
[1] AGH Univ Sci & Technol, Dept Appl Math, PL-30059 Krakow, Poland
[2] PN Lebedev Phys Inst, Dept Math Phys, Moscow 119991, Russia
[3] Univ Wroclaw, Inst Theoret Phys, PL-50204 Wroclaw, Poland
[4] AGH Univ Sci & Technol, Dept Min Geodes, PL-30059 Krakow, Poland
[5] Ivan Franko State Pedag Univ, Dept Econ Cybernet, Drogobych, Lviv Region, Ukraine
关键词
generalized Riemann type hydrodynamical equations; Whitham type dynamical systems; Hamiltonian systems; Lax type integrability; gradient-holonomic algorithm; EQUATION; MODEL;
D O I
10.3842/SIGMA.2010.002
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible Poisson structures and a Lax type representation for the special case N = 3 are constructed.
引用
收藏
页数:13
相关论文
共 28 条
[1]  
[Anonymous], 2000, MATH INTRO FLUID MEC
[2]  
[Anonymous], 1986, APPL LIE GROUPS DIFF
[3]  
Blaszak M., 1998, Texts and Monographs in Physics
[4]  
BOGOLYUBOV NN, 2009, IC2009095
[5]  
BOGOLYUBOV NN, 2007, IC2007109
[6]   On an integrable hierarchy derived from the isentropic gas dynamics [J].
Brunelli, JC ;
Das, A .
JOURNAL OF MATHEMATICAL PHYSICS, 2004, 45 (07) :2633-2645
[7]  
Davidson R., 1972, Methods in Nonlinear Plasma Theory
[8]  
Faddeev L. D., 2007, Hamiltonian Methods in the Theory of Solitons
[9]   SYMPLECTIC STRUCTURES, THEIR BACKLUND-TRANSFORMATIONS AND HEREDITARY SYMMETRIES [J].
FUCHSSTEINER, B ;
FOKAS, AS .
PHYSICA D, 1981, 4 (01) :47-66
[10]  
Gurevich A. V., 1988, Soviet Physics - JETP, V67, P1