ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Zemlyanukhin A. I. Exact soliton-like solution of the fifth-order nonlinear evolution equation. Izvestiya VUZ. Applied Nonlinear Dynamics, 1999, vol. 7, iss. 2, pp. 29-32. DOI: 10.18500/0869-6632-1999-7-2-29-32

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Language: 
Russian
Heading: 
Nonlinear Waves. Solitons
Article type: 
Article
UDC: 
534.222:539.3:532.5
DOI: 
10.18500/0869-6632-1999-7-2-29-32

Exact soliton-like solution of the fifth-order nonlinear evolution equation

Autors: 
Zemlyanukhin Aleksandr Isaevich, Yuri Gagarin State Technical University of Saratov
Abstract: 

Non-integrable fifth-order evolution equation, modelling wave process in nonlinear elastic dispersive media with moment stresses is investigated. The Backlund transformation and exact soliton - like solution are obtained for this equation.

Key words: 
-
Reference: 
  1. Engelbrecht YuK, Nigul UK. Nonlinear Waves of Deformation. М.: Nauka; 1981. 256 p. (in Russian).
  2. Zemlyanukhin АI, Mogilevitch LI. Nonlinear waves of deformations in cylindrical shells. Izvestiya VUZ. Applied Nonlinear Dynamics. 1995;3(1):52-58. (in Russian).
  3. Volmir AS. The Nonlinear Dynamics of Plates and Shells. Ohio: Wright-Patterson Air Force Base; 1974. 543 p.
  4. Kudryashov NА. Exact solutions of the non-linear wave equations arising in mechanics. J. Appl. Math. Mech. 1990;54(3):372-375. DOI: 10.1016/0021-8928(90)90140-6.
  5. Weiss J, Tabor M, Carnevale С. The Painleve property for partial differential equations. J. Math. Phys. 1983;24(3):522-526. DOI: 10.1063/1.525721.
  6. Kudryashov М, Zargaryan Е. Solitary waves in active—dissipative media. J. Phys. A: Math. Gen 1996;29(4):8067-8079. DOI: 10.1088/0305-4470/29/24/029.
  7. Ablowitz MJ, Segur H. Solitons and the Inverse Scattering Transform. Philadelfia: SIAM; 1981. 424 p. DOI: 10.1137/1.9781611970883.
  8. Olver PJ. Applications of Lie Groups to Differential Equations. N.Y.: Springer; 1986. 500 p. DOI: 10.1007/978-1-4684-0274-2.
Received: 
14.01.1999
Accepted: 
26.03.1999
Published: 
03.07.1999
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