Quasi-periodic lump chains for the generalized nonlocal Davey-Stewartson-type system

The quasi-periodic lump chains represent a distinctive spatial pattern in nonlinear integrable systems. This paper aims to investigate the construction and properties of such structures in nonlocal integrable systems like the generalized nonlocal Davey-Stewartson-type system. A systematic framework combining analytical and numerical methods is developed. Lumps are generated via the long wave limit, which are classified into three distinct types including bright, dark and four-petaled lumps. The existence condition of quasi-periodic lump chains is transformed into a nonlinear system of algebraic equations by introducing the Riemann-theta function that satisfies the Parity-time (PT)-symmetric condition. A generalized Levenberg-Marquardt algorithm is employed for solving this over-determined system. The quasi-periodic 1-lump chains are successfully derived and shown to exhibit the three types of quasi-periodic forms. Furthermore, the quasi-periodic lump chains degenerate into lump chains through asymptotic analysis. This study establishes an effective methodology for solving complex quasi-periodic solutions of the nonlocal integrable systems.