Darboux System: Liouville Reduction and an Explicit Solution
| Autor: | Alexey Borisovich Shabat, R. Ch. Kulaev, A. K. Pogrebkov |
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| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
Variables media_common.quotation_subject Construct (python library) Reduction (complexity) Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems Mathematics (miscellaneous) Factorization ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Linear problem Applied mathematics Mathematics media_common |
| Zdroj: | Proceedings of the Steklov Institute of Mathematics. 302:250-269 |
| ISSN: | 1531-8605 0081-5438 |
| Popis: | For a Darboux system in ℝ3, we introduce a class of solutions for which an auxiliary second-order linear problem satisfies the factorization condition. We show that this reduction provides the (local) solvability of the Darboux system, and present an explicit solution to this problem for two types of dependent variables. We also construct explicit formulas for the Lame coefficients and solutions to the associated linear problem. The previously known reduction to a weakly nonlinear system is shown to be a particular case of the approach proposed. |
| Databáze: | OpenAIRE |
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