On invariance properties of the wave equation
In: Journal of Mathematical Physics, Jg. 28 (1987-02-01), S. 307-318
Online
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Zugriff:
A complete group classification is given of both the wave equation c2(x)uxx−utt=0 (I) and its equivalent system vt=ux, c2(x)vx=ut (II) when the wave speed c(x)≠const. Equations (I) and (II) admit either a two‐ or four‐parameter group. For the exceptional case, c(x)=(Ax+B)2, equation (I) admits an infinite group. Equations (I) and (II) do not always admit the same group for a given c(x): The group for (I) can have more parameters or fewer parameters than that for (II); moreover, the groups can be different with the same number of parameters. Separately for (I) and (II), all possible c(x) that admit a four‐parameter group are found explicitly. The corresponding invariant (similarity) solutions are considered. Some of these wave speeds have realistic physical properties: c(x) varies monotonically from one positive constant to another positive constant as x goes from −∞ to +∞.
Titel: |
On invariance properties of the wave equation
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Autor/in / Beteiligte Person: | Kumei, Sukeyuki ; Bluman, George W. |
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Zeitschrift: | Journal of Mathematical Physics, Jg. 28 (1987-02-01), S. 307-318 |
Veröffentlichung: | AIP Publishing, 1987 |
Medientyp: | unknown |
ISSN: | 1089-7658 (print) ; 0022-2488 (print) |
DOI: | 10.1063/1.527659 |
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