Related papers: Nonabelian Integrable Systems, Quasideterminants, …
We study completely integrable systems attached to Takiff algebras $\mathfrak{g}_N$, extending open Toda systems of split simple Lie algebras $\mathfrak{g}$. With respect to Darboux coordinates on coadjoint orbits $\mathcal{O}$, the…
The formula of expanding the Abel variety theta function restricted to Abel subvariety into theta functions of this subvariety is obtained. With the help of this formula the solution of differential equations with Jacobi theta functions,…
A comprehensive algebro-geometric integration of the two component Nonlinear Vector Schr\"odinger equation (Manakov system) is developed. The allied spectral variety is a trigonal Riemann surface, which is described explicitly and the…
We discuss extension of soliton theories and integrable systems into noncommutative spaces. In the framework of noncommutative integrable hierarchy, we give infinite conserved quantities and exact soliton solutions for many noncommutative…
We construct soliton solutions for non-abelian loop Toda equations associated with general linear groups. Here we consider the untwisted case only and use the rational dressing method based upon appropriate block-matrix representation…
We further develop the approach to many-body systems based on finding conditions of existence of meromorphic solutions to certain linear partial differential and difference equations which serve as auxiliary linear problems for nonlinear…
We propose several different types of construction principles for new classes of Toda field theories based on root systems defined on Lorentzian lattices. In analogy to conformal and affine Toda theories based on root systems of semi-simple…
A class of rational solutions of Toda lattice satisfying certain Backlund transformations and a class of mixed rational-soliton solutions (quasisolitons) in wronskian formare obtained using the method of Ablowitz and Satsuma. Also an…
The relativistic Toda lattice equation is decomposed into three Toda systems, the Toda lattice itself, B\"acklund transformation of Toda lattice and discrete time Toda lattice. It is shown that the solutions of the equation are given in…
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…
Complexiton solutions (or complexitons for short) are exact solutions newly introduced to integrable equations. Starting with the solution classification for a linear differential equation, the Korteweg-de Vries equation and the Toda…
In a previous paper (Matsuno 2011 {\it J. Phys. A: Math. Theore.} {\bf 44} 495202), we have presented a determinantal expression of the bright $N$-soliton solution for a multi-component modified nonlinear Schr\"odinger (NLS) system with…
The discrete autonomous/non-autonomous Toda equations and the discrete Lotka-Volterra system are important integrable discrete systems in fields such as mathematical physics, mathematical biology and statistical physics. They also have…
We consider the relation between the discrete coupled nonlinear Schr\"{o}dinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schr\"{o}dinger equation. In the same way…
We apply an analogue of the Zakharov-Shabat dressing method to obtain infinite matrix solutions to the Toda lattice hierarchy. Using an operator transformation we convert some of these into solutions in terms of integral operators and…
In previous work the author found solutions to the Toda equations that were expressed in terms of determinants of integral operators. Here it is observed that a simple variant yields solutions to the matrix Toda equations. As an application…
In the article a classification method for nonlinear integrable equations with three independent variables is discussed based on the notion of the integrable reductions. We call the equation integrable if it admits a large class of…
We construct the classical W-algebras for some non-abelian Toda systems associated with the Lie groups GL(2n,R) and Sp(n,R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian…
The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by…
A system of linear integral equations is presented, which is the analog of the system of Marchenko integral equations, to solve the inverse scattering problem for the linear system associated with the derivative NLS equations. The…