4 papers
General tropical convergence of harmonic amoebas
Takashi Ichikawa
By using Schottky uniformization theory of degenerating algebraic curves, we describe the tropical convergence of harmonic amoebas of pointed Riemann surfaces to tropical curves wh…
Dimers for degenerating families of M-curves
Takashi Ichikawa
We study dimer models on infinite minimal graphs with Fock's weights for degenerating families of M-curves of any genus based on works of Boutillier-Cimasoni-de Tilière and Bobenko…
KP solitons and the Schottky uniformization
Takashi Ichikawa, Yuji Kodama
Real and regular soliton solutions of the KP hierarchy have been classified in terms of the totally nonnegative (TNN) Grassmannians. These solitons are referred to as KP solitons,…
Families of KP solutions associated with tropical curves having nontrivial weights
Takashi Ichikawa
In order to generalize a program by Agostini and others producing new KP solutions, we construct families of quasi-periodic KP solutions which are derived from degenerating Riemann…