Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2009-02-25
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Available at: http://publications.ictp.it
Scientific paper
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 two- and four-dimensional invariant reductions are studied in detail. The well defined regularization of the model is constructed and its Lax type integrability is discussed.
Nikolai Bogolubov Jr.
Golenia Jolanta
Gucwa Ilona
Prykarpatsky Anatoliy
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