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Solitary waves, homoclinic breather waves and rogue waves of the (3 + 1)-dimensional Hirota bilinear equation. (English) Zbl 1409.35180
Summary: In this paper, the (3 + 1)-dimensional Hirota bilinear equation is investigated, which can be used to describe the nonlinear dynamic behavior in physics. By using the Bell polynomials, the bilinear form of the equation is derived in a very natural way. Based on the resulting bilinear form, its \(N\)-solitary waves are further obtained by using the Hirota’s bilinear theory. Finally, by using the Homoclinic test method, we obtain its rational breather wave and rogue wave solutions, respectively. In order to better understand the dynamical behaviors of the equation, some graphical analyses are discussed for these exact solutions.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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