114 citations · 1.1k across the 53 of their papers we have counts for
53 papers
KP solitons and the Riemann theta functions
Yuji Kodama
We show that the -functions of the regular KP solitons from the totally nonnegative Grassmannians can be expressed by the Riemann theta functions on singular curves. We explicit…
On the full Kostant-Toda hierarchy and its -banded reductions for the Lie algebras of type and
Yuji Kodama, Yuancheng Xie
This paper concerns the solutions of the full Kostant-Toda (f-KT) hierarchy in the Hessenberg form and their reductions to the -banded Kostant-Toda (-KT) hierarchy. We…
Extended Schur's -functions and the full Kostant--Toda hierarchy on the Lie algebra of type
Yuji Kodama, Soichi Okada
The full Kostant--Toda hierarchy on a semisimple Lie algebra is a system of Lax equations, in which the flows are determined by the gradients of the Chevalley invariants.This paper…
Space Curves and Solitons of the KP Hierarchy. I. The -th Generalized KdV Hierarchy
Yuji Kodama, Yuancheng Xie
It is well known that algebro-geometric solutions of the KdV hierarchy are constructed from the Riemann theta functions associated with hyperelliptic curves, and that soliton solut…
Triangulations and soliton graphs for totally positive Grassmannian
Rachel Karpman, Yuji Kodama
The KP equation is a nonlinear dispersive wave equation which provides an excellent model for resonant interactions of shallow-water waves. It is well known that regular soliton so…
Optical Kerr spatiotemporal dark extreme waves
Stefan Wabnitz, Yuji Kodama, Fabio Baronio
We study the existence and propagation of multidimensional dark non-diffractive and non-dispersive spatiotemporal optical wave-packets in nonlinear Kerr media. We report analytical…