相关论文: Solutions for Toda systems on Riemann surfaces
Regularity properties of strong solutions are considered.
To the spectral curves of smooth periodic solutions of the $n$-wave equation the points with infinite energy are added. The resulting spaces are considered as generalized Riemann surfcae. In general the genus is equal to infinity,…
In this paper we study the existence of solutions to an isotropic differential inclusion.
We re-examine Shatalov-Sternin's proof of existence of resurgent solutions of a linear ODE. In particular, we take a closer look at the "Riemann surface" (actually, a two-dimensional complex manifold) whose existence, endless continuability…
In this paper, we prove existence of smooth solutions of the Navier-Stokes equations that gives a positive answer to the problem proposed by Fefferman [3].
We construct Toda brackets in unstable motivic homotopy theory and prove some fundamental properties of them. Furthermore we construct some examples of motivic Toda brackets.
We study a system of equations arising in the Chern-Simons model on finite graphs. Using the iteration scheme and the upper and lower solutions method, we get existence of solutions in the non-critical case. The critical case is dealt with…
A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two ``coupling'' matrices and is sufficiently general to include all Toda field theories existing in the literature. Lie point…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a continuous rational solution. This is known to fail in higher…
We show how to construct semi-invariants and integrals of the full symmetric sl(n) Toda lattice for all n. Using the Toda equations for the Lax eigenvector matrix we prove the existence of semi-invariants which are homogeneous coordinates…
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 establish new sufficient conditions for the existence of classical hyperbolic quasiperiodic solutions for natural Lagrangian system on Riemannian manifold with time-quasiperiodic force function
The main objective of the present work is to discuss the global existence and stability of solutions to the porous medium equations on Riemannian manifolds with singularities. Several different types of solutions are considered. Our proof…
The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the…
We consider the singular $SU(3)$ Toda system with multiple singular sources \begin{align*} \left\{\begin{array}{ll}-\Delta w_1=2e^{2w_1}-e^{w_2}+2\pi\sum_{\ell=1}^m\beta_{1,\ell}\delta_{P_{\ell}}\quad\text{in }\mathbb{R}^2\\…
We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two…
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…
We propose an analytical approach to the conformal mapping of (rectangular) polygons based on the theory of Riemann surfaces and theta functions.
We study a (2+1)-dimensional system that can be viewed as an infinite number of O(3) sigma-fields coupled by a nearest-neighbour Heisenberg-like interaction. We reduce the field equations of this model to an integrable system that is…