Related papers: The parametrix problem for Toda equation with step…
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 provide a rigorous treatment of the inverse scattering transform for the entire Toda hierarchy for solutions which are asymptotically close to (in general) different finite-gap solutions as $n\to\pm\infty$.
We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish…
We give an explicit formula for the solution to the initial value problem of the full symmetric Toda hierarchy. The formula is obtained by the orthogonalization procedure of Szeg\"{o}, and is also interpreted as a consequence of the QR…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
An analytic method for the solution of the evolution equation for GPDs is presented. The small x, xi asymptotics of GPDs are calculated.
A novel approach is proposed to characterize the dynamics of perturbed many-body integrable systems. Focusing on the paradigmatic case of the Toda chain under non-integrable Hamiltonian perturbations, this study introduces a method based…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed.
In this paper we consider the initial value problem for a family of shallow water equations on the line $\R$ with various asymptotic conditions at infinity. In particular we construct solutions with prescribed asymptotic expansion as…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…
We analyze solutions of the Toda system and establish an optimal Moser-Trudinger inequality
Critical points of semiclassical expansions of solutions to the dispersionful Toda hierarchy are considered and a double scaling limit method of regularization is formulated. The analogues of the critical points characterized by the strong…
This paper is devoted to the design of efficient primal-dual algorithm (PDA) for solving convex optimization problems with known saddle-point structure. We present a new PDA with larger acceptable range of parameters and correction, which…
A noncommutative version of the semi-discrete Toda equation is considered. A Lax pair and its Darboux transformations and binary Darboux transformations are found and they are used to construct two families of quasideterminant solutions.
Four problems about recovery of a high-frequency source in the one-dimension heat equation with homogeneous initial-boundary conditions by some information about partial asymptotic of its solution have solved. It is shown, that the source…
In this paper, we firstly construct a weakly coupled Toda lattices with indefinite metrics which consist of $2N$ different coupled Hamiltonian systems. Afterwards, we consider the iso-spectral manifolds of extended tridiagonal Hessenberg…
We consider the problem of recovering of initial data in the IBVP for the wave-type equation in the half-space by the solution restricted to the boundary. The singular value decomposition of this problem is concerned: the asymptotics of…
Orbital and asymptotic stability for 1-soliton solutions to the Toda lattice equations as well as small solitary waves to the FPU lattice equations are established in the energy space. Unlike analogous Hamiltonian PDEs, the lattice…
The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point $t_*$ and fast oscillating behavior after the point $t_*$. In the transition layer the behavior of the…