Asymptotic analysis of the higher-order lump in the Davey-Stewartson I equation

Abstract

In this paper, the long-time asymptotic dynamics of three types of the higher-order lump in the Davey-Stewartson I equation, namely the linear lump, triangular lump and quasi-diamond lump, are investigated. For large time, the linear lump splits into certain fundamental lumps arranged in a straight line, which are associated with root structures of the first component in used eigenvector. The triangular lump consists of certain fundamental lumps forming a triangular structure, which are described by the roots of a special Wronskian that is similar to Yablonskii-Vorob polynomial. The quasi-diamond lump comprises a diamond in the outer region and a triangular lump pattern in the inner region (if it exists), which are decided by the roots of a general Wronskain determinant. The minimum values of these lump hollows are dependent on time and approach zero when time goes to infinity. Our approximate lump patterns and true solutions show excellent agreement.