Abound rogue wave type solutions to the extended (3+1)-dimensional Jimbo–Miwa equation

Abstract

Under investigation in this article is an extended (3+1)-dimensional Jimbo–Miwa equation (JM), which can be used to describe many nonlinear phenomena in fluid dynamics. By using the Hirota bilinear form of the extended (3+1)-dimensional JM equation, thirty classes of rogue wave type solutions are found with the help of symbolic computations. The rogue wave type solutions contain two important parameters a and b. When a and b get different values, we can present obvious rogue wave type solutions. For example, (i) taking a=b=0, then we have algebraic solitary waves (lump); (ii) if one of a and b is fixed at 0 and the other is nonzero, then we have an interaction solution between an algebraically decayed soliton and exponentially decayed soliton (lumpoff); (iii) let a≠0 and b≠0, then we have an interaction solution between lump and exponentially localized twin soliton wave (instant or rogue wave). The new rogue wave type solutions help us to know different physical worlds.