Results 11 to 20 of about 78,766 (164)
On a solvable class of nonlinear difference equations of fourth order
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We consider a class of nonlinear difference equations of the fourth order, which extends some equations in the literature. It is shown that the class of equations is solvable in closed form explaining theoretically, among other things, solvability of ...
Stevo Stevic +3 more
doaj +1 more source
Solvability of a class of hyperbolic-cosine-type difference equations
Advances in Difference Equations, 2020 We describe a method for constructing one of the basic classes of solvable hyperbolic-cosine-type difference equations, generalizing a known difference equation by Laplace in a natural way.
Stevo Stević +3 more
doaj +1 more source
Electronic Journal of Qualitative Theory of Differential Equations, 2019 We introduce notion of a generalized invariant for difference equations, which naturally generalizes notion of an invariant for the equations. Some motivations, basic examples and methods for application of invariants in the theory of solvability of ...
Stevo Stevic
doaj +1 more source
Solvability of a one-parameter class of nonlinear second-order difference equations by invariants
Advances in Difference Equations, 2019 By using an invariant we show in an original and quite unexpected way that a one-parameter class of nonlinear second-order difference equations is solvable in closed form, improving and theoretically explaining a recent result in the literature.
Stevo Stević
doaj +1 more source
Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states [PDF]
, 2008 Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states.
Odake, Satoru, Sasaki, Ryu
core +3 more sources
New Quasi-Exactly Solvable Difference Equation [PDF]
Journal of Nonlinear Mathematical Physics, 2008 Exact solvability of two typical examples of the discrete quantum mechanics, i.e. the dynamics of the Meixner-Pollaczek and the continuous Hahn polynomials with full parameters, is newly demonstrated both at the Schroedinger and Heisenberg picture levels.
openaire +3 more sources
Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials [PDF]
, 1996 In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation.
Finkel, Federico +2 more
core +5 more sources
Electronic Journal of Qualitative Theory of Differential Equations, 2014 Well-defined solutions of the bilinear difference equation are represented in terms of generalized Fibonacci sequences and the initial value. Our results extend and give natural explanations of some recent results in the literature.
Stevo Stevic
doaj +1 more source
On some classes of solvable difference equations related to iteration processes
Electronic Journal of Qualitative Theory of Differential Equations, 2023 We present several classes of nonlinear difference equations solvable in closed form, which can be obtained from some known iteration processes, and for some of them we give some generalizations by presenting methods for constructing them.
Stevo Stevic
doaj +1 more source
A note on Burgers' turbulence [PDF]
, 1996 In this note the Polyakov equation [Phys. Rev. E {\bf 52} (1995) 6183] for the velocity-difference PDF, with the exciting force correlation function $\kappa (y)\sim1-y^{\alpha}$ is analyzed.
A. Chekhlov +9 more
core +3 more sources