Exotic localized structures based on variable separation solution of (2+1)-dimensional KdV equation via the extended tanh-function method

Abstract

In this paper, firstly, we obtain the variable separation solutions of (2 + 1)-dimensional KdV equation by the extended tanh-function method (ETM) based on mapping method. Novel localized coherent structures about multi-valued functions, i.e. special dromion, special peakon and foldon, and the interactions among them, are discussed. The interactions between two special dromions and between two special peakons possess novel property, that is, there exists a multi-valued foldon in the process of their collision, which is different from the reported cases in previous literature. Moreover, the explicit phase shifts for all the local excitations offered by the quantity u have been given, and are applied to these novel interactions in detail.