@article{eb6f82b73fe74e6c99c929980ab5dde4,
title = "In search of periodic solutions for a reduction of the Benney chain",
abstract = "We search for smooth periodic solutions for the system of quasi-linear equations known as the Lax dispersionless reduction of the Benney moments chain. It is naturally related to the existence of a polynomial in momenta integral for a classical Hamiltonian system with 1,5 degrees of freedom. For the solution in question, it is not known a priori if the system is elliptic or hyperbolic or of mixed type. We consider two possible regimes for the solution. The first is the case of only one real eigenvalue, where we can completely classify the solutions. The second case of strict hyperbolicity is really a challenge. We find a remarkable 2 × 2 reduction which is strictly hyperbolic with one umbilic point but violates the condition of genuine non-linearity.",
author = "Misha Bialy and Mironov, {Andrey E.}",
note = "Funding Information: It is a pleasure to thank Sasha Veselov, Misha Sodin, and Inna Scherbak for very useful discussions. It was very helpful to consult with Jenia Shustin who also kindly communicated to us a simple proof of Lemma 4.1 in Sec. IV. We are also grateful to Maxim Pavlov and the anonymous referee for providing the important references. M.B. was supported in part by ISF Grant No. 162/15 and A.E.M. was supported by RSF Grant No. 14-11-00441. It is our pleasure to thank these funds for the support.",
year = "2017",
month = nov,
day = "1",
doi = "10.1063/1.4991977",
language = "אנגלית",
volume = "58",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics",
number = "11",
}