Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power nonlinearities in n spatial dimensions: a radial wave equation, a radial Schrödinger equation and its derivative variant, and two proposed radial generalizations of modified Korteweg–de Vries equations, as well as Hamiltonian variants. The mains re...

A finite different scheme as well as least-square method is presented for the magneto-thermo analysis of an infinite functionally graded hollow cylinder. The radial displacement, mechanical stresses and temperature as well as the electromagnetic stress are investigated along the radial direction of the cylinder. Material properties are assumed to be graded in the radial direction according to a...

This paper derives and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. Th...

this paper is concerned with investigation of vertical impedance function of a surface rigid circular foundation resting on a semi-infinite transversely isotropic alluvium. to this end, the equations of motion in cylindrical coordinate system, which because of axissymmetry are two coupled equations, are converted into one partial differential equation using a method of potential function. the g...

Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-be...

We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the twodimensional (2D) cubic–quintic nonlinear Schrödinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, which allows one to effectively split the full 2D equation into radial and azimuthal 1D equations. A variation...

In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.

The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type inequalities.

The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type inequalities.