Related papers: On Psi-function for finite-gap potentials
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
In this article we give in analytical closed form the solutions of the Direchlet problems for the Laplace equations with inverse square and singular P\"oschl-Teller potentials
Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the…
In this work, we describe how to approximate solutions of some partial differential equations using the finite difference method defined on the Minkowski self-similar curve.
It is shown how to define difference equations on particular lattices $\{x_n\}$, $n\in\mathbb{Z}$, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special…
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
We compute the effective potential for $\phi^4$ theory with a squeezed coherent state type of construct for the ground state. The method essentially consists in optimising the basis at zero and finite temperatures. The gap equation becomes…
The aim of the present paper is to give extensions of the cosine-sine functional equation.
In the present article we describe a class of algebraic curves on which rational functions of two arguments may reach all their possible limiting values. We also solve a similar question for functions that can be represented as a uniform…
Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
We give a general expression of spherical functions on $p$-adic homogeneous spaces of $G$, based on data of $G$ and functional equations of spherical functions. Then, we show a unified method to obtain functional equations of spherical…
We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of…
We continue the study of positive singular solutions of PDEs arising from double phase functionals started in [6]. In particular, we consider the case $p<q < 2$, and we relax the assumption on the capacity of the singular set using an…
A spectral parameter power series (SPPS) representation for the regular solution of the radial Dirac system with complex coefficients is obtained, as well as a SPPS representation for the (entire) characteristic function of the…
Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $\kappa$ in the case of spin and pseudospin symmetry,…
In this paper, Sturm-Liouville problem for difference equations is considered with potential function q(n). The representations of solutions are obtained by variation of parameters method. These solutions are proved, using summation by…
We continue our solution of the inverse problem started by the first author in [Int. J. Mod. Phys. A 35, xxxx (2020), in production]. Additional potential functions for exactly solvable problems that correspond to the same energy spectrum…
In the paper, some lower bounds for polygamma functions are refined.
In present paper we suggest exact solution of the Poisson problem which appears in frequently addressed applications regarding calculation of the gravitational potential of spiral galaxies. We suggest an analytical solution for the problem…