Two-dimensional new coherent structures of lump-soliton solutions for the Mel'nikov equation

Under investigation in this paper are new novel coherent structures of two-dimensional lump-soliton for the Mel'nikov equation. The Hirota bilinear method and Kadomtsev-Petviashvili hierarchy reduction method are applied to construct a particular family of determinant semi-rational solutions exhibiting various coherent waves to the Mel'nikov equation. We first investigate some novel coherent waves, Nth-order lumps first appear from the (N + 1) dark line solitons and finally disappear into those (N + 1) dark line solitons after living on the constant background for a very short period. In contrast to the usual lump, those lumps in the coherent structures of lump-soliton are not only localized in two-dimensional space and but also localized in time.

Automated summary

This paper investigates the coherent structures of two-dimensional lump-solitons for the Mel'nikov equation, utilizing the Hirota bilinear method and Kadomtsev-Petviashvili hierarchy reduction method to construct specific solutions displaying various coherent waves. In contrast to traditional lumps, the lumps within the coherent structures of lump-solitons are localized not only in two-dimensional space but also in time.