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Complex potential equations I. A technique for solution
| Content Provider | Scilit |
|---|---|
| Author | Collins, C. B. |
| Copyright Year | 1976 |
| Description | This work amalgamates and solves certain problems arising in differential equation theory and in classical differential geometry.It describes a novel technique for solving systems of non-linear partial differential equations of the form where f(γ) and g(γ) are arbitrarily assigned functions. The circumstances are determined under which compatible solutions exist, not only when γ is real, but also when γ is complex, and all of the corresponding solutions are found. This is done by using a geometric technique that incorporates the equipotential surfaces of constant γ. In general, these surfaces are imaginary, and a fairly extensive treatment of such surfaces in (complexified) 3-dimensional Euclidean space is included. A close association is discovered between the set of equipotential surfaces and the class of surfaces of constant radii of principal normal curvature. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/ED724220941B50E7AAA778303F086B6D/S0305004100052798a.pdf/div-class-title-complex-potential-equations-i-a-technique-for-solution-div.pdf |
| Ending Page | 187 |
| Page Count | 23 |
| Starting Page | 165 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004100052798 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 1 |
| Volume Number | 80 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1976-07-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Applied Mathematics Equipotential Surfaces Differential Equation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
