Abstract
We construct various kinds of solutions to the elliptic cylindrical Kadomtsev–Petviashvili equation, which can be derived in the context of surface gravity waves. This investigation yields a diverse set of analytical outcomes, encompassing the dynamics of horseshoe-like solitons, lump chains, and lump waves. Based on the Hirota bilinear method, the lump chain is derived under specified conjugate constraint conditions. Additionally, we uncover three distinct types of novel interactions among lump waves through the utilization of the long wave limit method. A detailed analysis is conducted to elucidate the features and patterns inherent in these lump waves. The analytic findings presented may providing a descriptive framework for generic weakly nonlinear and weakly dispersive waves.
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