相关论文: Solutions for Toda systems on Riemann surfaces

In this note we apply the techniques of the toric systems introduced by Hille-Perling to several problems on smooth projective surfaces: We showed that the existence of full exceptional collection of line bundles implies the rationality for…

The existence of radially symmetric solutions is discussed for a Lane-Emden type system. This answer a question posed by da Silva and do O (2024). We also comment on the inhomogeneous version of the same system and discuss some open…

In this short review we compare different ways to construct solutions of the periodic Toda lattice. We give two recipes that follow from the projection method and compare them with the algebra-geometric construction of Krichever.

In this paper, we construct holomorphic families of Riemann surfaces from Veech groups and characterize their sections by some points of corresponding flat surfaces. The construction gives us concrete solutions for some Diophantine…

We find explicit (multisoliton) solutions for nonabelian integrable systems such as periodic Toda field equations, Langmuir equations, and Schrodinger equations for functions with values in any associative algebra. The solution for…

In the present paper we obtain some integrable generalisations of the Toda system generated by flat connection forms taking values in higher ${\bf Z}$--grading subspaces of a simple Lie algebra, and construct their general solutions. One…

We show that Toda lattices with the exceptional Cartan matrices are Liouville type systems. For these systems of equations, we obtain explicit formulas for the invariants and generalized Laplace invariants.

In recent works [hep-th/9909147, hep-th/0005259] was found a wonderful correlation between integrable systems and meromorphic functions. They reduce a problem of effictivisation of Riemann theorem about conformal maps to calculation of a…

This paper is the first in a forthcoming series of works where the authors study the global asymptotic behavior of the radial solutions of the 2D periodic Toda equation of type $A_n$. The principal issue is the connection formulae between…

We find integrals of motion for the recently introduced deformed Ruijsenaars-Schneider many-body system which is the dynamical system for poles of elliptic solutions to the Toda lattice with constraint of type B. Our method is based on the…

We find classical solutions to the simply-laced affine Toda equations which satisfy integrable boundary conditions using solitons which are analytically continued from imaginary coupling theories. Both static `vacuum' configurations and the…

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…

The purpose of these notes is to show that the methods introduced by Bauer and Furuta in order to refine the Seiberg-Witten invariants of smooth 4-dimensional manifolds can also be used to obtain stable homotopy classes from Riemann…

Under certain reality conditions, a general solution to the dispersionless Toda lattice hierarchy describes deformations of simply-connected plane domains with a smooth boundary. The solution depends on an arbitrary (real positive) function…

Integrable delay analogues of the two-dimensional Toda lattice equation are presented and their muti-soliton solutions are constructed by applying the delay reduction to the Gram determinant solution.

In this note we give a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial data.

In this paper, we study the blow-up analysis of an affine Toda system corresponding to minimal surfaces into ${\mathbb S}^4$ [19]. This system is an integrable system which is a natural generalization of sinh-Gordon equation [18]. By…

We study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures,…

We provide a rigorous treatment of the inverse scattering transform for the entire Toda hierarchy in the case of a quasi-periodic finite-gap background solution.

We present the necessary and sufficient conditions of the well-posedness of the initial value problem for certain fourth-order linear dispersive systems on the one-dimensional torus. This system is related with a dispersive flow for closed…