On invariance properties of the wave equation
A complete group classification is given of both the wave equation c 2(x)u x x −u t t =0 (I) and its equivalent system v t =u x , c 2(x)v x =u t (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)=(A x+B)2, equation...
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| Veröffentlicht in: | Journal of mathematical physics 1987-02, Vol.28 (2), p.307-318 |
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| container_title | Journal of mathematical physics |
| container_volume | 28 |
| creator | Bluman, George Kumei, Sukeyuki |
| description | A complete group classification is given of both the wave equation c
2(x)u
x
x
−u
t
t
=0 (I) and its equivalent system v
t
=u
x
, c
2(x)v
x
=u
t
(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)=(A
x+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 +∞. |
| doi_str_mv | 10.1063/1.527659 |
| format | Article |
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2(x)u
x
x
−u
t
t
=0 (I) and its equivalent system v
t
=u
x
, c
2(x)v
x
=u
t
(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)=(A
x+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 +∞.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.527659</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>Applied sciences ; Exact sciences and technology ; Other techniques and industries</subject><ispartof>Journal of mathematical physics, 1987-02, Vol.28 (2), p.307-318</ispartof><rights>American Institute of Physics</rights><rights>1988 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c322t-9041ead841298503179e96afce7246adf09ab7b29d299667d43cd793c1fa64833</citedby><cites>FETCH-LOGICAL-c322t-9041ead841298503179e96afce7246adf09ab7b29d299667d43cd793c1fa64833</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.527659$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,776,780,1553,27901,27902,76133</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=7529182$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Bluman, George</creatorcontrib><creatorcontrib>Kumei, Sukeyuki</creatorcontrib><title>On invariance properties of the wave equation</title><title>Journal of mathematical physics</title><description>A complete group classification is given of both the wave equation c
2(x)u
x
x
−u
t
t
=0 (I) and its equivalent system v
t
=u
x
, c
2(x)v
x
=u
t
(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)=(A
x+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 +∞.</description><subject>Applied sciences</subject><subject>Exact sciences and technology</subject><subject>Other techniques and industries</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1987</creationdate><recordtype>article</recordtype><recordid>eNp9z01LxDAQgOEgCtZV8Cf04EEPXTNJmo-jLK4KC3vRc5lNE4ysbU1qxX9vtdKL4Gnm8DDDS8g50CVQya9hWTIlS3NAMqDaFOOuD0lGKWMFE1ofk5OUXigF0EJkpNg2eWgGjAEb6_Iutp2LfXApb33eP7v8AweXu7d37EPbnJIjj_vkzn7ngjytbx9X98Vme_ewutkUljPWF4YKcFhrAczoknJQxhmJ3jrFhMTaU4M7tWOmZsZIqWrBba0Mt-BRCs35glxOd21sU4rOV10Mrxg_K6DVd2YF1ZQ50ouJdpgs7n0cO0KavSqZAc1GdjWxZEP_0zKToY3zuaqr_X_2z_svoeBrnQ</recordid><startdate>19870201</startdate><enddate>19870201</enddate><creator>Bluman, George</creator><creator>Kumei, Sukeyuki</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19870201</creationdate><title>On invariance properties of the wave equation</title><author>Bluman, George ; Kumei, Sukeyuki</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c322t-9041ead841298503179e96afce7246adf09ab7b29d299667d43cd793c1fa64833</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1987</creationdate><topic>Applied sciences</topic><topic>Exact sciences and technology</topic><topic>Other techniques and industries</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bluman, George</creatorcontrib><creatorcontrib>Kumei, Sukeyuki</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bluman, George</au><au>Kumei, Sukeyuki</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On invariance properties of the wave equation</atitle><jtitle>Journal of mathematical physics</jtitle><date>1987-02-01</date><risdate>1987</risdate><volume>28</volume><issue>2</issue><spage>307</spage><epage>318</epage><pages>307-318</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>A complete group classification is given of both the wave equation c
2(x)u
x
x
−u
t
t
=0 (I) and its equivalent system v
t
=u
x
, c
2(x)v
x
=u
t
(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)=(A
x+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 +∞.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.527659</doi><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 1987-02, Vol.28 (2), p.307-318 |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_crossref_primary_10_1063_1_527659 |
| source | AIP Digital Archive |
| subjects | Applied sciences Exact sciences and technology Other techniques and industries |
| title | On invariance properties of the wave equation |
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