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Russia Saratov
Year
2015
Volume
25
Issue
3
Pages
338-347
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Section Mathematics
Title Steady solitary wave solutions of the generalized sixth-order Boussinesq-Ostrovsky equation
Author(-s) Zemlyanukhin A.I.a, Bochkarev A.V.a
Affiliations Saratov State Technical Universitya
Abstract An overview of models that lead to the nonintegrable Ostrovsky equation and its generalizations having no exact solitary-wave solutions is given. A brief derivation of the Ostrovsky equation for longitudinal waves in a geometrically nonlinear rod lying on an elastic foundation is performed. It is shown that in the case of axially symmetric propagation of longitudinal waves in a physically nonlinear cylindrical shell interacting with a nonlinear elastic medium the displacement component obeys the generalized sixth-order Boussinesq-Ostrovsky equation. We construct an exact kink-like solution of this equation, establish a connection with the generalized nonlinear Schrödinger (GNLS) equation and find the steady travelling wave solution of the GNLS in the form of simple soliton with monotonic or oscillating tails.
Keywords nonlinear evolution equations, solitary-wave solutions, generalized nonlinear Schrödinger equation
UDC 517.95
MSC 34A05, 35C08, 35Q55, 74J35
DOI 10.20537/vm150304
Received 1 July 2015
Language English
Citation Zemlyanukhin A.I., Bochkarev A.V. Steady solitary wave solutions of the generalized sixth-order Boussinesq-Ostrovsky equation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 3, pp. 338-347.
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