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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2010, том 6, 002, 13 стр. (Mi sigma459)

Эта публикация цитируется в 21 статьях

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

Jołanta Goleniaa, Maxim V. Pavlovb, Ziemowit Popowiczc, Anatoliy K. Prykarpatskyda

a AGH University of Science and Technology
b Department of Mathematical Physics, P. N. Lebedev Physical Institute, 53 Leninskij Prospekt, Moscow 119991, Russia
c The Institute for Theoretical Physics, University of Wrocław, Wrocław 50204, Poland
d Department of Economical Cybernetics, Ivan Franko State Pedagogical University, Drohobych, Lviv Region, Ukraine

Аннотация: 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.

Ключевые слова: generalized Riemann type hydrodynamical equations; Whitham typedynamical systems; Hamiltonian systems; Lax type integrability;gradient-holonomic algorithm.

MSC: 35C05; 37K10

Поступила: 14 октября 2009 г.; в окончательном варианте 3 января 2010 г.; опубликована 7 января 2010 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2010.002



Реферативные базы данных:
ArXiv: 1001.1145


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