Publications (43)
Mach reflection and KP solitons in shallow water
Harry Yeh, Wenwen Li, Yuji Kodama
Reflection of an obliquely incident solitary wave onto a vertical wall is studied analytically and experimentally. We use the Kadomtsev-Petviashivili (KP) equation to analyze the e…
Fifty years of the finite nonperiodic Toda lattice: A geometric and topological viewpoint
Yuji Kodama, Barbara Shipman
In 1967, Japanese physicist Morikazu Toda published a pair of seminal papers in the Journal of the Physical Society of Japan that exhibited soliton solutions to a chain of particle…
Cohomology of real Grassmann manifold and KP flow
Luis Casian, Yuji Kodama
We consider a realization of the real Grassmann manifold Gr(k,n) based on a particular flow defined by the corresponding (singular) solution of the KP equation. Then we show that t…
Toda Hierarchy with Indefinite Metric
Yuji Kodama, Jian Ye
We consider a generalization of the full symmetric Toda hierarchy where the matrix of the Lax pair is given by , with a full symmetric matrix and a…
KP solitons and total positivity for the Grassmannian
Yuji Kodama, Lauren Williams
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional dispersive wave equation now known as the KP equation.…
The Pfaff lattice on symplectic matrices
Yuji Kodama, Virgil U. Pierce
The Pfaff lattice is an integrable system arising from the SR-group factorization in an analogous way to how the Toda lattice arises from the QR-group factorization. In our recent…
Regularizations for shock and rarefaction waves in the perturbed solitons of the KP equation
Guangfu Han, Yuji Kodama, Chuanzhong Li +1
Using an asymptotic perturbation method, we study the initial value problem for the KP equation with initial data consisting of parts of exact line-soliton solutions. We consider a…
KP solitons in shallow water
Yuji Kodama
The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The classification is based on the far-…
KP solitons, total positivity, and cluster algebras
Yuji Kodama, Lauren Williams
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional nonlinear dispersive wave equation now known as the KP…
On a family of solutions of the KP equation which also satisfy the Toda lattice hierarchy
Gino Biondini, Yuji Kodama
We describe the interaction pattern in the - plane for a family of soliton solutions of the Kadomtsev-Petviashvili (KP) equation, . Tho…
The Deodhar decomposition of the Grassmannian and the regularity of KP solitons
Yuji Kodama, Lauren Williams
Given a point A in the real Grassmannian, it is well-known that one can construct a soliton solution u_A(x,y,t) to the KP equation. The contour plot of such a solution provides a t…
On the Whitham Equations for the Defocusing Complex Modified KdV Equation
Yuji Kodama, V. U. Pierce, Fei-Ran Tian
We study the Whitham equations for the defocusing complex modified KdV (mKdV) equation. These Whitham equations are quasilinear hyperbolic equations and they describe the averaged…
Combinatorics of dispersionless integrable systems and universality in random matrix theory
Yuji Kodama, Virgil U. Pierce
It is well-known that the partition function of the unitary ensembles of random matrices is given by a tau-function of the Toda lattice hierarchy and those of the orthogonal and sy…
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…
The full Kostant-Toda hierarchy on the positive flag variety
Yuji Kodama, Lauren Williams
We study some geometric and combinatorial aspects of the solution to the full Kostant-Toda (f-KT) hierarchy, when the initial data is given by an arbitrary point on the totally non…
Spectral stability and time evolution of N-solitons in KdV hierarchy
Yuji Kodama, Dmitry Pelinovsky
This paper concerns spectral stability and time evolution of -solitons in the KdV hierarchy with mixed commuting time flows. Spectral stability problem is analyzed by using a pa…
Numerical study of the KP equation for non-periodic waves
Chiu-Yen Kao, Yuji Kodama
The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact s…
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…
Combinatorics of KP solitons from the real Grassmannian
Yuji Kodama, Lauren Williams
Given a point A in the real Grassmannian, it is well-known that one can construct a soliton solution u_A(x,y,t) to the KP equation. The contour plot of such a solution provides a t…
Non-crossing permutations for the KP solitons under the Gel'fand-Dickey reductions and the vertex operators
Shilong Huang, Yuji Kodama, Chuanzhong Li
We give a classification of the soliton solutions of the KP hierarchy, referred to as the , under the Gel'fand-Dickey -reductions in terms of the permu…
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…
Normal Form, Symmetry and Infinite Dimensional Lie Algebra for System of Ode's
Yuji Kodama
The normal form for a system of ode's is constructed from its polynomial symmetries of the linear part of the system, which is assumed to be semi-simple. The symmetries are shown t…
The Whitham Equations for Optical Communications: Mathematical Theory of NRZ
Yuji Kodama
We present a model of optical communication system for high-bit-rate data transmission in the nonreturn-to-zero (NRZ) format over transoceanic distance. The system operates in a sm…
Compactification of the isospectral varieties of nilpotent Toda lattices
Luis Casian, Yuji Kodama
The paper concerns a compactification of the isospectral varieties of nilpotent Toda lattices for real split simple Lie algebras. The compactification is obtained by taking the clo…
Soliton solutions of the KP equation and application to shallow water waves
Sarvarish Chakravarty, Yuji Kodama
The main purpose of this paper is to give a survey of recent development on a classification of soliton solutions of the KP equation. The paper is self-contained, and we give a com…
Toda lattice, cohomology of compact Lie groups and finite Chevalley groups
Luis Casian, Yuji Kodama
In this paper, we describe a connection that exists among (a) the number of singular points along the trajectory of Toda flow, (b) the cohomology of a compact subgroup , and (c)…
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 explici…
Young diagrams and N-soliton solutions of the KP equation
Yuji Kodama
We consider -soliton solutions of the KP equation, (-4u_t+u_{xxx}+6uu_x)_x+3u_{yy}=0 . An -soliton solution is a solution which has the same set of line solito…
A generating function for the N-soliton solutions of the Kadomtsev-Petviashvili II equation
Sarbarish Chakravarty, Yuji Kodama
This work describes a classification of the -soliton solutions of the Kadomtsev-Petviashvili II equation in terms of chord diagrams of N chords joining pairs of 2N points. The d…
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…
KP solitons and Mach reflection in shallow water
Yuji Kodama
This gives a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili equation with an emphasis on the Mach reflection problem in shallow water.
Soliton Solutions of the KP Equation with V-Shape Initial Waves
Yuji Kodama, Masayuki Oikawa, Hidekazu Tsuji
We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same a…
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,…
Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
Shogo Aoyama, Yuji Kodama
Based on the dispersionless KP (dKP) theory, we give a comprehensive study of the topological Landau-Ginzburg (LG) theory characterized by a rational potential. Writing the dKP hie…
Iso-spectral deformations of general matrix and their reductions on Lie algebras
Yuji Kodama, Jian Ye
We study an iso-spectral deformation of general matrix which is a natural generalization of the Toda lattice equation. We prove the integrability of the deformation, and give an ex…
Toda lattices with indefinite metric II: Topology of the iso-spectral manifolds
Yuji Kodama, Jian Ye
We consider the iso-spectral real manifolds of tridiagonal Hessenberg matrices with real eigenvalues. The manifolds are described by the iso-spectral flows of indefinite Toda latti…
Construction of KP solitons from wave patterns
Sarbarish Chakravarty, Yuji Kodama
We often observe that waves on the surface of shallow water form complex web-like patterns. They are examples of nonlinear waves, and these patterns are generated by nonlinear inte…
On the Whitham equations for the defocusing nonlinear Schrodinger equation with step initial data
Gino Biondini, Yuji Kodama
The behavior of solutions of the finite-genus Whitham equations for the weak dispersion limit of the defocusing nonlinear Schrodinger equation is investigated analytically and nume…
On the cohomology of real Grassmann manifolds
Luis Casian, Yuji Kodama
We give an explicit and simple construction of the incidence graph for the integral cohomology of real Grassmann manifold Gr(k,n) in terms of the Young diagrams filled with the let…
Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function
Yuji Kodama, Shigeki Matsutani, Emma Previato
M. Toda in 1967 (\textit{J. Phys. Soc. Japan}, \textbf{22} and \textbf{23}) considered a lattice model with exponential interaction and proved, as suggested by the Fermi-Pasta-Ulam…
The Finite Non-periodic Toda Lattice: A Geometric and Topological Viewpoint
Yuji Kodama, Barbara Shipman
In 1967, Japanese physicist Morikazu Toda published the seminal papers exhibiting soliton solutions to a chain of particles with nonlinear interactions between nearest neighbors. I…
Classification of the line-soliton solutions of KPII
Sarbarish Chakravarty, Yuji Kodama
In the previous papers (notably, Y. Kodama, J. Phys. A 37, 11169-11190 (2004), and G. Biondini and S. Chakravarty, J. Math. Phys. 47 033514 (2006)), we found a large variety of lin…
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…