Linear cases of Bragg-Hawthorne equation for steady axisymmetric incompressible ideal flows are systematically discussed. The equation is converted to a more convenient form in a spherical coordinate system. A new vorticity decomposition is derived. General solutions for 16 linear cases of the equation are obtained. These solutions can be specified to gain new analytical vortex flows, as examples in the paper demonstrate. A lot of well-known solutions like potential flow past a sphere, Hill's vortex with and without swirl, are included and extended in these solutions. Special relations between some vortex flows are also revealed when exploring or comparing related solutions.
The attempt of this paper is to suggest a new theoretical medium to support the e®orts of building particle models as mechanical¯eld structures. The medium model is based on two simple fundamental assumptions. All the properties of the medium, as counterparts in this medium of the well-known physics laws, including energy and momentum conservations, Lorentz transformation and special relativity, electromagnetic interaction, etc., are derived from these two assumptions. The governing equations are established based on the derived properties. Some steady solutions as well as the feasibility of interpreting these solutions as particles are also brie°y discussed.
Consideration in this paper is the Cauchy problem of a generalized hyperelastic-rod wave equation. We first derive a wave-breaking mechanism for strong solutions, which occurs in finite time for certain initial profiles. In addition, we determine the existence of some new peaked solitary wave solutions.
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