Related papers: Schur algorithm for Stieltjes indefinite moment pr…
We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schr\"odinger equation. We prove that a particular class of integrators are conjugate to unitary methods for…
A nested Schur complement solver is proposed for iterative solution of linear systems arising in exponential and implicit time integration of the Maxwell equations with perfectly matched layer (PML) nonreflecting boundary conditions. These…
In this paper, we first investigate the global existence of a solution for the stochastic fractional nonlinear Schr\"odinger equation with radially symmetric initial data in a suitable energy space $H^{\alpha}$. We then show that the…
We consider the linear and non linear cubic Schr\"odinger equations with periodic boundary conditions, and their approximations by splitting methods. We prove that for a dense set of arbitrary small time steps, there exists numerical…
We describe a fast solver for linear systems with reconstructable Cauchy-like structure, which requires O(rn^2) floating point operations and O(rn) memory locations, where n is the size of the matrix and r its displacement rank. The solver…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
It is known in the case of the Stieltjes transform that evaluating the integral by expanding the kernel of transformation followed by term by term integration leads to an infinite series of divergent integrals. Moreover, it is known that…
By applying a simple symmetry reduction on a two-layer liquid model, a nonlocal counterpart of it is obtained. Then a general form of nonlocal nonlinear Schrodinger (NNLS) equation with shifted parity, charge-conjugate and delayed time…
We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well-known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger's results a…
A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed: (1) motivated by an analogy with the Camassa-Holm equation a class of isospectral…
We present a new asymptotic formula for the Stieltjes constants which is both simpler and more accurate than several others published in the literature (see e.g. \cite{Fekih-Ahmed}, \cite{Knessl Coffey}, \cite{Paris}). More importantly, it…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
We introduce a new strategy in solving the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed \emph{moment}…
Matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schr\"odinger equation with nonvanishing boundary conditions. It is shown that the initial value problem can be solved exactly. The…
We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schr\"odinger equations with a real drift.
A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…
A review of a recent method is presented to construct certain exact solutions to the focusing nonlinear Schr\"odinger equation on the line with a cubic nonlinearity. With motivation by the inverse scattering transform and help from the…
A linear operator $S$ in a complex Hilbert space $\hh$ for which the set $\dzn{S}$ of its $C^\infty$-vectors is dense in $\hh$ and $\{\|S^n f\|^2\}_{n=0}^\infty$ is a Stieltjes moment sequence for every $f \in \dzn{S}$ is said to generate…
Inter alia, we present a Fourier series involving the generalised Stieltjes constants.
We consider polynomials of the form $\operatorname{s}_\lambda(y_1^{[\varkappa_1]},\ldots,y_n^{[\varkappa_n]})$, where $\lambda$ is an integer partition, $\operatorname{s}_\lambda$ is the Schur polynomial associated to $\lambda$, and…