Exact traveling wave profiles are here obtained for a general reaction-diffusionconvection equation, a two-phase flow equation, a generalized HarryαDym equa-Ε½ . tion, a generalized Kortewegαde Vries KdV equation, a modified mKdV equation, a branching network model equation, a Nagumo equation, and a
Vortex dynamics for the nonlinear wave equation
β Scribed by Fang Hua Lin
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 386 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0010-3640
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β¦ Synopsis
Vortex dynamics for the nonlinear wave equation is a typical model of the "particle and field" theories of classical physics. The formal derivation of the dynamical law was done by J. Neu. He also made an interesting connection between vortex dynamics and the Dirac theory of electrons. Here we give a rigorous mathematical proof of this natural dynamical law.
π SIMILAR VOLUMES
We show uniqueness of sufficiently regular solutions to critical semilinear wave equations and wave maps in the (a priori) much larger class of distribution solutions with finite energy, assuming only that the energy is nonincreasing in time.
The existence and estimate of the upper bound of the Hausdorff dimension of the global attractor for the strongly damped nonlinear wave equation with the Dirichlet boundary condition are considered by introducing a new norm in the phase space. The gained Hausdorff dimension decreases as the damping