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SOLUTIONS NEAR SINGULAR POINTS TO THE EIKONAL AND RELATED FIRST ORDER NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS IN TWO INDEPENDENT VARIABLES
| Content Provider | Semantic Scholar |
|---|---|
| Author | Howard, Ralph Martinsson, Per-Gunnar |
| Copyright Year | 2000 |
| Abstract | A detailed study of solutions to the first order partial differential equation H(x, y, zx, zy) = 0, with special emphasis on the eikonal equation z x + z 2 y = h(x, y), is made near points where the equation becomes singular in the sense that dH = 0, in which case the method of characteristics does not apply. The main results are that there is a strong lack of uniqueness of solutions near such points and that solutions can be less regular than both the function H and the initial data of the problem, but that this loss of regularity only occurs along a pair of curves through the singular point. The main tools are symplectic geometry and the Sternberg normal form for Hamiltonian vector fields. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://people.math.sc.edu/howard/Reprints/eikonal_abstract.pdf |
| Alternate Webpage(s) | http://people.math.sc.edu/howard/Reprints/eikonal.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0001172v1.pdf |
| Alternate Webpage(s) | http://www.math.sc.edu/~howard/Reprints/eikonal.pdf |
| Alternate Webpage(s) | http://www.math.sc.edu/~howard/Reprints/eikonal.ps.gz |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Hamiltonian (quantum mechanics) Singular Solutions Symplectic integrator |
| Content Type | Text |
| Resource Type | Article |
