We study a charged and massive scalar field in the background of Nutku-Ghezelbash-Kumar metric which is obtained by addition time coordinate to Nutku helicoid non-trivial way. The angular part Klein-Gordon equation can be written as double confluent Heun equation. radial cannot solved terms known function its general form. However, some special cases, also explicitly full numerically observe th...

The joint distribution of a geometric Brownian motion and its time-integral was derived in seminal paper by Yor (1992) using Lamperti’s transformation, leading to explicit solutions terms modified Bessel functions. In this paper, we revisit classic result the simple Laplace transform approach connection Heun differential equation. We extend methodology with affine drift show that process can be...

In this paper, we obtain the metric of space-time generated by a charged and rotating gravitational body surrounded loud strings, namely, Kerr–Newman black hole with addition cloud strings. background, find radial solutions Dirac equation for massive particles show that they are given in terms Generalized Heun functions. The dependence these on parameter codifies presence strings is pointed out.

Abstract We consider the discrete defocusing nonlinear Schrödinger equation in its integrable version, which is called Ablowitz–Ladik lattice. periodic boundary conditions with period N and initial data sampled according to Generalized Gibbs ensemble. In this setting, Lax matrix of lattice a random CMV-periodic it related Killip-Nenciu Circular $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/...

The generic Heun operator of Lie type is identified as a certain $BC$-Gaudin magnet Hamiltonian in magnetic field. By using the modified algebraic Bethe ansatz introduced to diagonalize such Gaudin models, we obtain spectrum terms roots inhomogeneous equations. We show also that these are intimately associated polynomial solutions differential equation. illustrate use this approach two contexts...

In this paper we study the relativistic scalar particle described by Klein-Gordon interacts with uniform magnetic field in context of Som-Raychaudhuri space-time. Based on property biconfluent Heun function equation, corresponding oscillator and generalized under considering Coulomb potential are separately investigated, analogue Aharonov-Bohm effect is analyzed scenario. On basis, also give in...