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A nonlinear vibration system behaviors always periodically; however, sometimes a vibrating structure, e.g. an empty oil tank, will be collapsed suddenly. This can be explained as a kind of rogue waves. This paper gives a general approach to search for rational breather waves to nonlinear equations including nonlinear vibration systems and dispersive wave systems. A breather type of rogue wave solution which contains two peaks whose amplitudes are two to three times higher than its surrounding waves and generally forms in a short time is constructed. Moreover, by using three-wave method, new breather-type multisolitary coherent structures are presented, the fusion interactions of localized structures are discussed and graphically investigated, showing some novel features and interesting behaviors. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the (3+1)-dimensional potential-YTSF equation is investigated. Exact solutions with three-wave form including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave solutions are obtained using Hirota’s bilinear form and generalized three-wave approach with the aid of symbolic computation. Moreover, the properties for some new solutions are shown with some figures. [Copyright &y& Elsevier]

Abstract: Exact three-wave solutions including periodic cross-kink wave solutions, doubly periodic solitary wave solutions and breather type of two-solitary wave solutions for the (3+1)-dimensional Jimbo–Miwa equation are obtained using the generalized three-wave method. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving high-dimensional nonlinear evolution equations in mathematical physics. [Copyright &y& Elsevier]