Related papers: SDYM equations on the self-dual background
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex…
Hyperspectral unmixing is an important remote sensing task with applications including material identification and analysis. Characteristic spectral features make many pure materials identifiable from their visible-to-infrared spectra, but…
We give explicit formulas for a pair of linearly independent solutions of $(py')'(x)+q(x)=(\lambda_1r_1(x)+\cdots+\lambda_dr_d(x))y(x)$, thus generalizing to arbitrary $d$ previously known formulas for $d=1$. These are power series in the…
Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order…
The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…
We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration.…
In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose…
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.
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial…
In this paper, we propose some algorithms for analytical solution construction to nonlinear polynomial partial differential equations with constant function coefficients. These schemes are based on one-(single), two- (double) or three-…
We introduce a fully nonlinear PDE with a differential form $\Lambda$, which unifies several important equations in K\"ahler geometry including Monge-Amp\`ere equations, J-equations, inverse $\sigma_{k}$ equations, and the deformed…
Feynman integrals are solutions to linear partial differential equations with polynomial coefficients. Using a triangle integral with general exponents as a case in point, we compare $D$-module methods to dedicated methods developed for…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
We study 2D discrete integrable equations of order 1 with respect to one independent variable and $m$ with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…