A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Geng, Xianguo; Zhai, Yunyun; Xue, Bo; Wei, Jiao
• Is Part Of: Journal of nonlinear mathematical physics. Volume 26:Issue 1(2019)
• Page Start: 1
• Page End: 23
• Publication Date: 2019-01-02
• Subjects: long wave-short wave type equations -- Baker-Akhiezer function -- meromorphic function -- quasiperiodic solutions; 37K40 -- 37K20 -- 14H42; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2019.1544785
• Languages: English
• ISSNs: 1402-9251

Abstract

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