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Russia Saratov
Section  Mathematics 
Title  Steady solitary wave solutions of the generalized sixthorder BoussinesqOstrovsky equation 
Author(s)  Zemlyanukhin A.I.^{a}, Bochkarev A.V.^{a} 
Affiliations  Saratov State Technical University^{a} 
Abstract  An overview of models that lead to the nonintegrable Ostrovsky equation and its generalizations having no exact solitarywave 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 sixthorder BoussinesqOstrovsky equation. We construct an exact kinklike 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, solitarywave 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 sixthorder BoussinesqOstrovsky equation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 3, pp. 338347. 
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