Algebro-geometric integration of a modified shallow wave hierarchy
2021 ◽
Vol 0
(0)
◽
Keyword(s):
Abstract By introducing two sets of Lenard recursion relations, we derive a hierarchy of modified shallow wave equations associated with a 3 × 3 matrix spectral problem with three potentials from the zero-curvature equation. The Baker–Akhiezer function and two meromorphic functions are defined on the trigonal curve which is introduced by utilizing the characteristic polynomial of the Lax matrix. Analyzing the asymptotic properties of the Baker–Akhiezer function and two meromorphic functions at two infinite points, we arrive at the explicit algebro-geometric solutions for the entire hierarchy in terms of the Riemann theta function by showing the explicit forms of the normalized Abelian differentials of the third kind.
2017 ◽
Vol 18
(2)
◽
pp. 129-136
2016 ◽
Vol 15
(05)
◽
pp. 667-697
◽
1997 ◽
Vol 110
(1)
◽
pp. 47-56
◽
2017 ◽
Vol 2017
◽
pp. 1-9
◽
2020 ◽
Vol 0
(0)
◽
2010 ◽
Vol 24
(08)
◽
pp. 791-805
◽
1997 ◽
pp. 158-161