On Genus-Two Solutions for the ILW equation

Abstract

The existence of theta function solutions of genus two for the ILW equation is established. A numerical example is also presented. The method basically goes along with the Krichever's construction of theta function solutions for soliton equations, such as the KP equation. This idea leads us to a question whether a Riemann surface exists which allows a peculiar Abelian integral of the third kind. The answer is affirmative at least for genus-two curves.

arXiv comment15 pages, 4 figures

References in corpus (1)

• The ILW hierarchy

Cited by in corpus (1)

• On the non-chiral intermediate long wave equation II: periodic case