A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions are identified in the de-terministic limit. The polygon solutions, of relevance to on-lattice Eden growth from a seed in the zero-noise limit, are unstable in ...

Starting with the S-wave radial equation for an attractive central potential V (r), we give results for the n(principal quantum number) and the μ (reduced mass) dependence of Rn0(0), the S-wave radial waveunction at the origin, for potentials with definite curvature.

The thin-disc global asymptotics are discussed for axisymmetric meanfield dynamos with vacuum boundary conditions allowing for non-local terms arising from a finite radial component of the mean magnetic field at the disc surface. This leads to an integro-differential operator in the equation for the radial distribution of the mean magnetic field strength, Q(r) in the disc plane

In this note we propose a new set of coordinates to study the hyperbolic or non-elliptic cubic nonlinear Schrödinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically radial standing waves, as well as hyperbolically radial self-similar solutions. Many of the arguments can easily be adapted to more general nonlinearities.

It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so that the spherical coordinates can be separated in terms of angular spinors like in special relativity, obtaining a pair of radial equations and a specific ...

The main purpose of the present paper is the heuristic study of the structure, properties and consequences of new class of potential functions results from the concept of pq-Radial functions which are fundamental family of solutions of second order pq-PDE. Keyword: Potential functions, Laplace equation, pq-Radial function, pq-PDE, Legendre polynomials

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian (−∆) with s ∈ (0, 1) for any space dimensions N > 1. By extending a monotonicity formula found by Cabré and Sire [9], we show that the linear equation (−∆)u+ V u = 0 in R has at most one radial and bounded solution vanishing at infinity, provided that the potential V is ...

In this paper, we consider radial standing waves to a nonlinear Klein-Gordon equation with repulsive inverse-square potential. It is known that there exist “radial” ground states the stationary problem of equation. Here, are non-trivial solutions having least energy among all We deal stability and instability state waves.

In this paper, the effect of initial stress on the radial vibrations of elastic hollow cylinder with rotation is discussed. The one-dimensional equation of elastodynamic is solved in terms of radial displacement. The frequency equation is obtained when the boundaries are free; fixed and mixed boundary condition is examined numerically. The determination is concerned with the eigenvalues of the ...

*Correspondence: Jeong Ryeol Choi, Department of Radiologic Technology, Daegu Health College, Yeongsongro 15, Buk-gu, Daegu 702-722, Republic of Korea e-mail: [email protected] Quantum characteristics of a charged particle traveling under the influence of an external time-dependent magnetic field in ionized plasma are investigated using the invariant operator method. The Hamiltonian that gi...