A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation
- https://doi.org/10.1080/14029251.2019.1544785How to use a DOI?
- long wave-short wave type equations, Baker-Akhiezer function, meromorphic function, quasi-periodic solutions
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.
- © 2019 The Authors. Published by Atlantis and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Xianguo Geng AU - Yunyun Zhai AU - Bo Xue AU - Jiao Wei PY - 2021 DA - 2021/01 TI - A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation JO - Journal of Nonlinear Mathematical Physics SP - 1 EP - 23 VL - 26 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2019.1544785 DO - https://doi.org/10.1080/14029251.2019.1544785 ID - Geng2021 ER -