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Abstract A generalized Calogero–Bogoyavlenskii–Schiff equation is considered, and based on its Hirota bilinear form, a class of lump solutions is explicitly generated via symbolic computations with Maple, together with plots of a specific lump solution. The result enlarges the category of nonlinear partial differential equations which possess lump solutions. [ABSTRACT FROM AUTHOR]

A bilinear form of a nonisospectral differential-difference equation related to the Ablowitz-Ladik (AL) spectral problem is derived by a transformation of dependent variables. Exact solutions to the resulting bilinear equation are found. The -soliton-like solutions and the double Casoratian solutions are derived by means of Hirota's direct method and the double Casoratian technique, respectively. Moreover, the connection between those two classes of solutions is explored. [ABSTRACT FROM AUTHOR]