The Solution of Embedding Problems in the Framework of GAPs with Applications on Nonlinear PDEs
The paper presents a special class of embedding problems whoes solutions are important for the explicit solution of nonlinear partial differential equations. It is shown that these embedding problems are solvable and explicit solutions are given. Not only are the solutions new but also the mathemati...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2009/120213 |
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| Summary: | The paper presents a special class of embedding problems whoes solutions are important for the explicit solution of nonlinear partial differential equations. It is shown that these embedding problems are solvable and explicit solutions are given. Not only are the solutions new but also the mathematical framework of their
construction which is defined by a nonstandard function theory built over nonstandard algebraical structures, denoted as “GAPs”. These GAPs must not be neither associative nor division algebras, but the corresponding function theories built over them preserve the most important symmetries from the classical complex function theory in a generalized form: a generalization of the Cauchy-Riemannian differential equations exists as well as a generalization of the classical Cauchy Integral Theorem. |
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| ISSN: | 1687-9120 1687-9139 |