an:06011740
Zbl 1232.35143
Knyazev, M. A.
Kink-type states in the Sharma-Tasso-Olver model
EN
Russ. Phys. J. 54, No. 3, 391-392 (2011); translation from Izv. Vyssh. Uchebn. Zaved., Fiz., No. 3, 111-112 (2011).
00287447
2011
j
35Q51 35C08
kink; Sharma-Tasso-Olver equation; Hirota method
From the text: The nonlinear model for soliton-like objects (for example kinks) described by the Sharma-Tasso-Olver (STO) equation is considered. Different solutions of this equation and its properties have been investigated in ample detail [\textit{S. Wang, X.-Y. Tang} and \textit{S.-Y. Lou}, Chaos Solitons Fractals 21, No. 1, 231--239 (2004; Zbl 1046.35093); \textit{Z.-J. Lian} and \textit{S.Y. Lou}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 63, No. 5--7, A, e1167--e1177 (2005; Zbl 1224.37038); \textit{B. Erba??} and \textit{E. Yusufo??lu}, Chaos Solitons Fractals 41, No. 5, 2326--2330 (2009; Zbl 1198.81087); \textit{A. Chen}, ``Multi-kink solutions and soliton fission and fusion of Sharma-Tasso-Olver equation'', Phys. Lett., A 374, No. 23, 2340--2345 (2010)]. It has been demonstrated that the equation is integrable in the sense of existence of the Lax pair of operators. Its solutions in the form of soliton (kink) and a bound state of two solitons were obtained. Because the examined problem is urgent, search for new exact solutions is of great interest. In the present work, new solutions for the STO equation which describe kink-like states are constructed by the Hirota method [\textit{M. J. Ablowitz} and \textit{H. Segur}, Solitony i metod obratnoj zadachi (Russian). Moskva: ``Mir'' (1987; Zbl 0621.35003); translation of: Solitons and the inverse scattering transform. SIAM Studies in Applied Mathematics, 4. Philadelphia: SIAM (1981; Zbl 0472.35002)].
Zbl 1046.35093; Zbl 1224.37038; Zbl 1198.81087; Zbl 0621.35003; Zbl 0472.35002