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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas
Ian. M. Anderson, Mark E. Fels Utah State University, Logan Utah, USA
Аннотация:
To every Darboux integrable system there is an associated Lie group $G$ which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of Lie type for the Vessiot group $G$. If the Vessiot group $G$ is solvable then the Cauchy problem can be solved by quadratures. This allows us to give explicit integral formulas, similar to the well known d'Alembert's formula for the wave equation, to the initial value problem with generic non-characteristic initial data.
Ключевые слова:
Cauchy problem; Darboux integrability; exterior differential systems; d'Alembert's formula.
Поступила: 8 октября 2012 г.; в окончательном варианте 20 февраля 2013 г.; опубликована 27 февраля 2013 г.
Образец цитирования:
Ian. M. Anderson, Mark E. Fels, “The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas”, SIGMA, 9 (2013), 017, 22 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma800 https://www.mathnet.ru/rus/sigma/v9/p17
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