Related papers: A variational Analysis of the Toda System on Compa…
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 solve a super Toda system on a closed Riemann surface of genus~$\gamma>1$ and with some particular spin structures. This generalizes the min-max methods and results for super Liouville equations and gives new existence results for super…
In a previous paper, the author proved the existence of extremal function for the Moser-Trudinger inequality on a compact manifold. In the this paper, we will give a new proof of one of the key proposition.
Given a compact closed four dimensional smooth Riemannian manifold, we prove existence of extremal functions for Moser-Trudinger type inequality. The method used is Blow-up analysis combined with capacity techniques.
The main aim of this article is to study non-singular version of Moser-Trudinger and Adams-Moser-Trudinger inequalities and the singular version of Moser-Trudinger equality in the Cartesian product of Sobolev spaces. As an application of…
A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…
We study a sharp fractional Moser-Trudinger type inequality in dimension 1, its compactness properties and the critical points of a functional associeted to the inequality.
This paper has two purposes. The first is to classify all those versions of the Toda equations which govern the existence of $\tau$-primitive harmonic maps from a surface into a homogeneous space $G/T$ for which $G$ is a noncomplex…
Building on and extending tools from variational analysis, we prove Kuratowski convergence of sets of simplicial area minimizers to minimizers of the smooth Douglas-Plateau problem under simplicial refinement. This convergence is with…
Let $(\Sigma, g_1)$ be a compact Riemann surface with conical singularites of angles in $(0, 2\pi)$, and $f: \Sigma\to\mathbb R$ be a positive smooth function. In this paper, by establishing a sharp quantization result, we prove the…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
In this paper we continue our study of the geometric properties of full symmetric Toda systems from \cite{CSS14,CSS17,CSS19}. Namely we describe here a simple geometric construction of a commutative family of vector fields on compact…
On the 3-dimensional fractional-order Toda lattice with two controls The main purpose of this paper is to study the fractional-order system with Caputo derivative associated to 3-dimensional Toda lattice with two controls. For this…
Originally a model for wave propagation on the line, the Toda lattice is a wonderful case study in mechanics and symplectic geometry. In Flaschka's variables, it becomes an evolution given by a Lax pair on the vector space of real,…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
On a Riemann surface with a holomorphic $r$-differential, one can naturally define a Toda equation and a cyclic Higgs bundle with a grading. A solution of the Toda equation is equivalent to a harmonic metric of the Higgs bundle for which…
This paper is devoted to the Moser-Trudinger inequality on smooth riemanniansurfaces. We establish that the constants involved can be chosen to depend on only 3parameters, which are the systole, isoperimetric constant and curvature of the…
We consider equal-mass periodic Toda oscillators with balanced loss-gain for two and three particles. The two-particle system is integrable with the Hamiltonian and the genralized total momentum being two integrals of motion. The model in…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
In this paper we consider the unstable chaotic attractor of the Toda potential and stabilize it by a control in integral form. In order to obtain stability results, we propose a special technique which is based on the idea of reduction of…