Geodesic
Steady solitary wave solutions of the generalized sixth-order Boussinesq--Ostrovsky equation
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 3, pp. 338-347

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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. 
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     author = {A. I. Zemlyanukhin and A. V. Bochkarev},
     title = {Steady solitary wave solutions of the generalized sixth-order {Boussinesq--Ostrovsky} equation},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     url = {http://geodesic.mathdoc.fr/item/VUU_2015_25_3_a3/}
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A. I. Zemlyanukhin; A. V. Bochkarev. Steady solitary wave solutions of the generalized sixth-order Boussinesq--Ostrovsky equation. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 3, pp. 338-347. http://geodesic.mathdoc.fr/item/VUU_2015_25_3_a3/