Abstract
This paper aims to explore a kind of lump solutions in nonlinear dispersive waves with higher-order rational dispersion relations. We show that the second member in the commuting Kadomtsev–Petviashvili hierarchy is such an example, and construct its lump solutions, based on a Hirota trilinear form. The presented lump solutions have one peak and two valleys, where the global maximum and minimum values are achieved. A few three-dimensional plots and contour plots are made for a specific example of the lumps.
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