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A class of lump solutions of (2+1)-dimensional Boussinesq equation are obtained with the help of Maple by using Hirota bilinear method. Some contour plots with different determinant values are sequentially made to show that the corresponding lump solution tends to zero when the determinant approaches zero. The particular lump solutions with specific values of the involved parameters are plotted, as illustrative examples.

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a b s t r a c t In this paper, the nonlinear dispersive Zakharov-Kuznetsov equation is solved by using the auxiliary equation method. As a result, new solitary pattern, solitary wave and singular solitary wave solutions are found.

Soliton molecules have become one of the hot topics in recent years. In this article, we investigate soliton molecules and some novel hybrid solutions for the (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt (gKDKK) equation by using the velocity resonance, module resonance, and long wave limits methods. By selecting some specific parameters, we can obtain soliton molecules and asymmetric soliton molecules of the gKDKK equation. And the interactions among N-soliton molecules are elastic. Furthermore, some novel hybrid solutions of the gKDKK equation can be obtained, which are composed of lumps, breathers, soliton molecules and asymmetric soliton molecules. Finally, the images of soliton molecules and some novel hybrid solutions are given, and their dynamic behavior is analyzed.