تقرير
Hierarchy of coupled Burgers-like equations induced by conditional symmetries
| العنوان: | Hierarchy of coupled Burgers-like equations induced by conditional symmetries |
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| المؤلفون: | Gorgone, M., Oliveri, F., Sgroi, E. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 35K10 - 58J70 - 58J72 |
| الوصف: | It is known that $Q$-conditional symmetries of the classical Burgers' equation express in terms of three functions satisfying a coupled system of Burgers-like equations. The search of conditional symmetries of this system leads to a system of five coupled Burgers-like equations. Iterating the procedure, an infinite hierarchy of systems made of an odd number of coupled Burgers-like equations is obtained. Moreover, starting from a pair of Burgers-like equations, a similar hierarchy of systems made of an even number of coupled Burgers-like equations arises; it is also proved that the two hierarchies may be unified. Writing a generic element of this hierarchy as a matrix Burgers' equation, the existence of the matrix Hopf-Cole transformation allows for its linearization and the determination of its solution. Finally, it is shown that each element of the hierarchy possesses a five-dimensional Lie algebra of classical point symmetries. Though these Lie algebras are realized in manifolds with different dimensionality, they are all isomorphic. Comment: 27 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.06381 |
| رقم الأكسشن: | edsarx.2407.06381 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |