Generation of anomalously scattered lump waves for (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

Abstract

The anomalous scattering of lump waves governed by the Date–Jimbo–Kashiwara–Miwa (DJKM) equation is explored via two distinct methods. The second-order anomalously scattered lump is derived by degenerating the M-lump solution under the limit of infinite phase. Higher order anomalously scattered lumps are obtained through the degeneration of lump chains described by infinite periods, with analyses of two types of degenerate lump chains. A thorough asymptotic analysis is employed to investigate both the dynamic behavior and scattering angles of the anomalous scattering phnomena. Notably, the triangular structures of higher order lumps are found to be closely related to the Yablonskii-Vorob’ev polynomials. These insights may deepen our understanding of the intrinsic characteristics of lump waves.