相关论文: Solution of the generalized periodic discrete Toda…

Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…

We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer…

We construct soliton solutions for non-abelian loop Toda equations associated with general linear groups. Here we consider the untwisted case only and use the rational dressing method based upon appropriate block-matrix representation…

This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…

A set of coupled conditions consisting of differential-difference equations is presented for Casorati determinants to solve the Toda lattice equation. One class of the resulting conditions leads to an approach for constructing complexiton…

Based on a Riemann theta function and the super-Hirota bilinear form, we propose a key formula for explicitly constructing quasi-periodic wave solutions of the supersymmetric Ito's equation in superspace $\mathbb{C}_{\Lambda}^{2,1}$. Once a…

In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give…

In this manuscript, we address the resolution of conformable Gegenbauer differential equations. We demonstrate that our solution aligns precisely with the results obtained through the power series approach. Furthermore, we delve into the…

We develop a monotonicity formula for solutions of the fractional Toda system $$ (-\Delta)^s f_\alpha = e^{-(f_{\alpha+1}-f_\alpha)} - e^{-(f_\alpha-f_{\alpha-1})} \quad \text{in} \ \ \mathbb R^n,$$ when $0<s<1$, $\alpha=1,\cdots,Q$,…

A method is proposed to systematically generate solutions of the two-dimensional Toda lattice equation in terms of previously known solutions $\phi\left(x,y\right)$ of the two-dimensional Laplace's equation. The two-dimensional solution of…

The paper introduces a novel Ito's formula for time dependent tempered generalized functions. As an application, we study the heat equation when initial conditions are allowed to be a generalized tempered function. A new proof of the…

We prove separation of variables for the most general (Dn type) periodic Toda lattice with 2x2 Lax matrix. It is achieved by finding proper normalisation for the corresponding Baker-Akhiezer function. Separation of variables for all other…

We solve the inverse spectral problem associated with periodic conservative multi-peakon solutions of the Camassa-Holm equation. The corresponding isospectral sets can be identified with finite dimensional tori.

This note contains a short proof of the functional equation for the zeta function.

We introduce two types bilateral zeta functions, which are related to the primitive and normalized multiple sine functions respectively. Further, we establish their main properties, that is, Fourier expansions, analytic continuations,…

We give a transformation formula for the ``2nd order'' mock theta function which was recently proposed in connection with the quantum invariant for the Seifert manifold.

We prove that a certain sequence of tau functions of the Garnier system satisfies Toda equation. We construct a class of algebraic solutions of the system by the use of Toda equation; then show that the associated tau functions are…

In this paper, we aim for the theta function representation of quasi-periodic solution and related crucial quantities for a two-component generalization of Burgers equation. Our tools include the theory of algebraic curve, the meromorphic…

This paper gives out the general solutions of variable coefficients ODE and Riccati equation by way of integral series E(X) and F(X). Such kinds of integral series are the generalized form of exponential function, and keep the properties of…

This paper develops one of the methods for study of nonlinear Partial Differential equations. We generalize Sato equation and represent the algorithm for construction of some classes of nonlinear Partial Differential Equations (PDE)…