相关论文: Affine Toda system of $\mathbf{A}$ and $\mathbf{C}…

It has been established that the local mass of blow-up solutions to Toda systems associated with the simple Lie algebras $\mathbf{A}_n,~\mathbf{B}_n,~\mathbf{C}_n$ and $\mathbf{G}_2$ can be represented by a finite Weyl group. In particular,…

In this article we obtain total masses of solutions to the Toda system associated to a general simple Lie algebra with singular sources at the origin. The determination of such total masses is one of the important steps towards establishing…

Toda systems are generalizations of the Liouville equation to systems using simple Lie algebras. We study the blowup phenomena of their solutions by giving concrete examples demonstrating blowup masses corresponding to the Weyl groups.

For Toda systems with Cartan matrix either $B_2$ or $G_2$, we prove that the local mass of blowup solutions at its blowup points converges to a finite set. Further more this finite set can be completely determined for $B_2$ Toda systems,…

For all rank two Toda systems with an arbitrary singular source, we use a unified approach to prove: (i) The pair of local masses $(\sigma_1,\sigma_2)$ at each blowup point has the expression $$\sigma_i=2(N_{i1}\mu_1+N_{i2}\mu_2+N_{i3}),$$…

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…

The masses of affine Toda theories are known to correspond to the entries of a Perron-Frobenius eigenvector of the relevant Cartan matrix. The Lagrangian of the theory can be expressed in terms of a suitable eigenvector of a Coxeter element…

In this paper, the classification in [Lin,Wei,Ye] of solutions to Toda systems of type $A$ with singular sources is generalized to Toda systems of types $C$ and $B$. Like in the $A$ case, the solution space is shown to be parametrized by…

We study the singularities (blow-ups) of the Toda lattice associated with a real split semisimple Lie algebra $\mathfrak g$. It turns out that the total number of blow-up points along trajectories of the Toda lattice is given by the number…

A cross between two well-known integrable multi-particle dynamics, an affine Toda molecule and a Sutherland system, is introduced for any affine root system. Though it is not completely integrable but partially integrable, or quasi exactly…

In this note, we consider blow-up for solutions of the SU(3) Toda system on a compact surface \Sigma. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang and we extend it to the case of…

We present a definition of the non-abelian generalisations of affine Toda theory related from the outset to vertex operator constructions of the corresponding Kac-Moody algebra $\gh$. Reuslts concerning conjugacy classes of the Weyl group…

We consider the so-called Toda system in a smooth planar domain under homogeneous Dirichlet boundary conditions. We prove the existence of a continuum of solutions for which both components blow-up at the same point. This blow-up behavior…

Many integrable theories can be formulated universally in terms of Lie algebraic root systems. Well-studied are conformally invariant scalar field theories of Toda type and their massive versions, which can be expressed in terms of simple…

In this article we prove that for locally defined singular SU(n+1) Toda systems in R^2, the profile of fully bubbling solutions near the singular source can be accurately approximated by global solutions. The main ingredients of our new…

Motivated by the study of non abelian Chern Simons vortices of non topological type in Gauge Field Theory, we analyse the solvability of planar Liouville systems of Toda type in presence of singular sources. We identify necessary and…

We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac-Moody root system $\tilde{A}_n$, generalizing the theory of multiple Dirichlet series for finite Weyl groups. The construction is…

In this paper, we study general Toda systems with homogeneous Neumann boundary conditions on Riemann surfaces. Assuming the surface satisfies the ``$k$-symmetric'' condition, we construct a family of bubbling solutions using singular…

Following a prescription of \cite{4} for a solitonic specialization of the general solutions to the (abelian) periodic Toda field theories, we discuss a construction of the soliton solutions for a wide class of two-dimensional completely…

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…