Lie algebraic methods and solutions of linear partial differential equations. (English) Zbl 0729.35028
Summary: An algebraic method to obtain the solution of linear partial differential equations of evolution type is discussed. The proposed method exploits the Lie differential operators and their matrix realization, to reduce the equation to an easily solvable generalized matrix form. Some applications to problems of specific interest are also discussed.
MSC:
35G05 | Linear higher-order PDEs |
35G10 | Initial value problems for linear higher-order PDEs |
35K25 | Higher-order parabolic equations |
17B99 | Lie algebras and Lie superalgebras |
References:
[1] | DOI: 10.1007/BF03024106 · JFM 55.1029.01 · doi:10.1007/BF03024106 |
[2] | DOI: 10.2307/1967773 · JFM 50.0297.01 · doi:10.2307/1967773 |
[3] | DOI: 10.2307/1967773 · JFM 50.0297.01 · doi:10.2307/1967773 |
[4] | Schrödinger E., Proc. R. Ir. Acad. Sect. A 46 pp 9– (1940) |
[5] | DOI: 10.2140/pjm.1955.5.1033 · Zbl 0067.29401 · doi:10.2140/pjm.1955.5.1033 |
[6] | DOI: 10.2140/pjm.1955.5.1033 · Zbl 0067.29401 · doi:10.2140/pjm.1955.5.1033 |
[7] | DOI: 10.1016/0022-0396(77)90088-2 · Zbl 0329.35010 · doi:10.1016/0022-0396(77)90088-2 |
[8] | DOI: 10.1063/1.1705306 · Zbl 0173.29604 · doi:10.1063/1.1705306 |
[9] | DOI: 10.1007/BF02724503 · doi:10.1007/BF02724503 |
[10] | DOI: 10.1007/BF02723075 · doi:10.1007/BF02723075 |
[11] | DOI: 10.1063/1.528100 · Zbl 0785.22027 · doi:10.1063/1.528100 |
[12] | DOI: 10.1063/1.1666533 · Zbl 0286.35025 · doi:10.1063/1.1666533 |
[13] | DOI: 10.1063/1.529020 · Zbl 0709.70014 · doi:10.1063/1.529020 |
[14] | DOI: 10.1063/1.529020 · Zbl 0709.70014 · doi:10.1063/1.529020 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.