A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation

Based on the Lenard recursion relation and zero-curvature equation, we derive a hierarchy of long wave-short wave type equations associated with 3 × matrix spectral problem three potentials. Resorting to characteristic polynomial Lax matrix, trigonal curve is defined, which Baker-Akhiezer function two meromorphic functions are introduced. Analyzing some properties functions, including asymptotic expansions at infinite points, obtain essential singularities divisor function. Utilizing theory algebraic curves, quasi-periodic solutions for entire finally derived in terms Riemann theta