The construction of special solutions to partial differential equations

Peter J. Olver; Philip Rosenau

doi:10.1016/0375-9601(86)90534-7

The construction of special solutions to partial differential equations

Peter J. Olver, Philip Rosenau

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

Almost all the methods devised to date for constructing particular solutions to a partial differential equation can be viewed as manifestations of a single unifying method characterized by the appending of suitable "side conditions" to the equation, and solving the resulting overdetermined system of partial differential equations. These side conditions can also be regarded as specifying the invariance of the particular solutions under some generalized group of transformations.

Original language	English (US)
Pages (from-to)	107-112
Number of pages	6
Journal	Physics Letters A
Volume	114
Issue number	3
DOIs	https://doi.org/10.1016/0375-9601(86)90534-7
State	Published - Feb 10 1986

Bibliographical note

Funding Information:
1 Supported in part by NSF Grant MCS 81-00786.

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10.1016/0375-9601(86)90534-7

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author = "Olver, {Peter J.} and Philip Rosenau",

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AB - Almost all the methods devised to date for constructing particular solutions to a partial differential equation can be viewed as manifestations of a single unifying method characterized by the appending of suitable "side conditions" to the equation, and solving the resulting overdetermined system of partial differential equations. These side conditions can also be regarded as specifying the invariance of the particular solutions under some generalized group of transformations.

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The construction of special solutions to partial differential equations

Abstract

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