11 Result(s)
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Article
On a Bernoulli-integrable magnetohydrodynamic system
A geometric procedure is used to isolate four Bernoulli integrals for a nonlinear, two-dimensional magnetohydrodynamic system. The general solution of the latter may thereby be constructed.
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Article
Termination of Bergman series. Connection to the Bn Toda System
Truncation of Bergman-type series applied to a canonical hyperbolic equation is shown to lead to the integrable Bn Toda lattice. In particular, the recurrence relations for the truncated Bergman series are implie...
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Article
Group invariance of a neo-Hookean system: incorporation of stretch change
Invariance of the nonlinear elasto-static system descriptive of the plane-strain deformation of a neo-Hookean material is determined under Lie group transformations which accommodate change in stretch. The ass...
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Article
Exact solutions for vertical drainage and redistribution in soils
We solve a versatile nonlinear convection-diffusion model for nonhysteretic redistribution of liquid in a finite vertical unsaturated porous column. With zero-flux boundary conditions, the nonlinear boundary-v...
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Article
On a nonlinear moving boundary problem with heterogeneity: application of a reciprocal transformation
A nonlinear problem of Stefan-type is analysed. An exact solution is obtained by means of a reciprocal transformation.
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Article
Padé extension of Bergman-series solutions to nonlinear boundary-value problems in heat conduction
Bergman-type series solutions involving iterated complementary error integrals are constructed for nonlinear boundary-value problems associated with heat conduction in a region bounded internally by a cylindri...
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Article
Antiplane crack problems for an inhomogeneous elastic material
This paper examines some antiplane crack problems in an elastic material with variable shear modulus. An expression for the energy release rate is obtained for each of the cracks considered and a comparison ma...
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Article
Cylindrical impact waves in inhomogeneous viscoelastic media
A detailed study is presented of cylindrical shear waves in inhomogeneous Maxwellian viscoelastic materials whose parameters depend continuously on a single radial coordinate. A formal asymptotic technique is ...
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Article
Transient displacement and stress in non-homogeneous elastic shells
Transient displacement and stress in thick inhomogeneous cylindrical and spherical shells is investigated for situations when the surfaces are subjected to dynamic loads consistent with the production of radia...
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Article
Antiplane deformations of inhomogeneous elastic materials
The system of equations governing antiplane deformations of inhomogeneous elastic media is examined with a view to achieving its reduction to a canonical form associated with the Cauchy-Riemann system.
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Article
On reduction properties in the theory of lubrication
In the case of constant film thickness, Reynolds' equation of plane lubrication theory reduces to Laplace's equation for the pressure distribution. In this paper, non-constant forms for the film thickness are ...
