Classification of quasi-periodic lump chains to the generalized Davey–Stewartson-type system

Abstract

Classification of quasi-periodic lump chains to the generalized Davey–Stewartson-type system is studied by combining the Hirota’s bilinear form with the Riemann-theta function. The quasi-periodic lump chains solvability problem can be formulated into an overdetermined system, which can be solved using the Gauss–Newton method. In particular, single lump can be categorized into three main types including bright lump, four-petaled lump and dark lump. Furthermore, by constraining the range of ${\lambda }^2$, this classification can be further refined, yielding bright quasi-periodic lump chains, four-petaled quasi-periodic lump chains and dark quasi-periodic lump chains. Additionally, certain dynamic behaviors of the quasi-periodic lump chains are explored. These new structures enrich the phenomena of nonlinear waves.