Resumen de Bilinear Form, N Solitons, Breathers and Periodic Waves for a (3+1)-Dimensional Korteweg-de Vries Equation with the Time-Dependent Coefficients in a Fluid
Chun Hui Feng, Bo Tian, Xiao Tian Gao
Korteweg-de Vries-type equations have occurred in the fields of planetary oceans, atmospheres, cosmic plasmas and so on, while nonlinear evolution equations with the variable coefficients have provided a realistic perspective on the inhomogeneities of media and non-uniformities of boundaries. In this paper, we investigate a (3+1)- dimensional Korteweg-de Vries equation with the time-dependent coefficients in a fluid. Based on the Hirota method, we obtain a bilinear form via the binary Bell polynomial approach. Based on the bilinear form, we derive the N-soliton, breather and periodic-wave solutions, where N is a positive integer. Besides, we investigate the asymptotic behaviors of the breather and periodic-wave solutions. Breather waves and periodic waves are graphically displayed. Finally, relation between the periodicwave solutions and one-soliton solutions is discussed. This paper provides an intuitive understanding for the nonlinear phenomena of those obtained solutions, and those nonlinear phenomena have potential application value in fluid dynamics and other fields.
