M. G. Makhmudova, A. Kh. Khanmamedov, “Asymptotic periodic solution of the Cauchy problem for the Langmuir lattice”, Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 12,Pages <nobr>2049

This article is cited in 2 papers

Asymptotic periodic solution of the Cauchy problem for the Langmuir lattice

M. G. Makhmudova^a, A. Kh. Khanmamedov^ba

^a Baku State University, ul. Z. Khalilova 23, Baku, AZ1148, Azerbaijan
^b Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, ul. B. Vahabzade 9, Baku, AZ1141, Azerbaijan

Abstract: The Cauchy problem for the Langmuir lattice with the initial condition in the form of the sum of a periodic and a rapidly decreasing sequences is studied by the method of inverse scattering problem. A method for constructing a periodic solution of the Langmuir lattice from a known periodic solution is proposed. The existence of an asymptotically periodic solution is proven.

Key words: Langmuir lattice, Cauchy problem, asymptotic periodic solution, theory of existence of solution.

UDC: 519.642.8

Received: 18.03.2014

DOI: 10.7868/S004446691512008X