Algebraic resolution of the Burgers equation with a forcing term
We introduce an inhomogeneous term, f ( t , x ), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f ( t , x ) which depend nontrivially on both t and x , we find that there i...
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| Veröffentlicht in: | Pramāṇa 2017-05, Vol.88 (5), p.1-6, Article 74 |
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| creator | SINUVASAN, R TAMIZHMANI, K M L LEACH, P G |
| description | We introduce an inhomogeneous term,
f
(
t
,
x
), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions
f
(
t
,
x
) which depend nontrivially on both
t
and
x
, we find that there is just one symmetry. If
f
is a function of only
x
, there are three symmetries with the algebra
s
l
(2,
R
). When
f
is a function of only
t
, there are five symmetries with the algebra
s
l
(2,
R
) ⊕
s
2
A
1
. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient. |
| doi_str_mv | 10.1007/s12043-017-1382-3 |
| format | Article |
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f
(
t
,
x
), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions
f
(
t
,
x
) which depend nontrivially on both
t
and
x
, we find that there is just one symmetry. If
f
is a function of only
x
, there are three symmetries with the algebra
s
l
(2,
R
). When
f
is a function of only
t
, there are five symmetries with the algebra
s
l
(2,
R
) ⊕
s
2
A
1
. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.</description><identifier>ISSN: 0304-4289</identifier><identifier>EISSN: 0973-7111</identifier><identifier>DOI: 10.1007/s12043-017-1382-3</identifier><language>eng</language><publisher>New Delhi: Springer India</publisher><subject>Algebra ; Astronomy ; Astrophysics and Astroparticles ; Burgers equation ; Linear equations ; Mathematical analysis ; Observations and Techniques ; Physics ; Physics and Astronomy ; Symmetry</subject><ispartof>Pramāṇa, 2017-05, Vol.88 (5), p.1-6, Article 74</ispartof><rights>Indian Academy of Sciences 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-957253ff61f6e40548426ab32b609b2ef94848cb15cfd410854d4d9e4ef1e5893</citedby><cites>FETCH-LOGICAL-c316t-957253ff61f6e40548426ab32b609b2ef94848cb15cfd410854d4d9e4ef1e5893</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12043-017-1382-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12043-017-1382-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>SINUVASAN, R</creatorcontrib><creatorcontrib>TAMIZHMANI, K M</creatorcontrib><creatorcontrib>L LEACH, P G</creatorcontrib><title>Algebraic resolution of the Burgers equation with a forcing term</title><title>Pramāṇa</title><addtitle>Pramana - J Phys</addtitle><description>We introduce an inhomogeneous term,
f
(
t
,
x
), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions
f
(
t
,
x
) which depend nontrivially on both
t
and
x
, we find that there is just one symmetry. If
f
is a function of only
x
, there are three symmetries with the algebra
s
l
(2,
R
). When
f
is a function of only
t
, there are five symmetries with the algebra
s
l
(2,
R
) ⊕
s
2
A
1
. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.</description><subject>Algebra</subject><subject>Astronomy</subject><subject>Astrophysics and Astroparticles</subject><subject>Burgers equation</subject><subject>Linear equations</subject><subject>Mathematical analysis</subject><subject>Observations and Techniques</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Symmetry</subject><issn>0304-4289</issn><issn>0973-7111</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kEtPwzAQhC0EEqXwA7hZ4mzw-pHYN0rFS6rEBc5Wkq7bVG3c2okQ_x6XcODCaVejmVntR8g18FvgvLxLILiSjEPJQBrB5AmZcFtKVgLAad4lV0wJY8_JRUobzsEqqSfkfrZdYR2rtqERU9gOfRs6Gjzt10gfhrjCmCgehupH_2z7Na2oD7FpuxXtMe4uyZmvtgmvfueUfDw9vs9f2OLt-XU-W7BGQtEzq0uhpfcF-AIV18ooUVS1FHXBbS3Q26yYpgbd-KUCbrRaqqVFhR5QGyun5Gbs3cdwGDD1bhOG2OWTDozRojAgy-yC0dXEkFJE7_ax3VXxywF3R1BuBOUyKHcE5WTOiDGTsrfLD_9p_jf0DS41ab0</recordid><startdate>20170501</startdate><enddate>20170501</enddate><creator>SINUVASAN, R</creator><creator>TAMIZHMANI, K M</creator><creator>L LEACH, P G</creator><general>Springer India</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170501</creationdate><title>Algebraic resolution of the Burgers equation with a forcing term</title><author>SINUVASAN, R ; TAMIZHMANI, K M ; L LEACH, P G</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-957253ff61f6e40548426ab32b609b2ef94848cb15cfd410854d4d9e4ef1e5893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Astronomy</topic><topic>Astrophysics and Astroparticles</topic><topic>Burgers equation</topic><topic>Linear equations</topic><topic>Mathematical analysis</topic><topic>Observations and Techniques</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Symmetry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>SINUVASAN, R</creatorcontrib><creatorcontrib>TAMIZHMANI, K M</creatorcontrib><creatorcontrib>L LEACH, P G</creatorcontrib><collection>CrossRef</collection><jtitle>Pramāṇa</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>SINUVASAN, R</au><au>TAMIZHMANI, K M</au><au>L LEACH, P G</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Algebraic resolution of the Burgers equation with a forcing term</atitle><jtitle>Pramāṇa</jtitle><stitle>Pramana - J Phys</stitle><date>2017-05-01</date><risdate>2017</risdate><volume>88</volume><issue>5</issue><spage>1</spage><epage>6</epage><pages>1-6</pages><artnum>74</artnum><issn>0304-4289</issn><eissn>0973-7111</eissn><abstract>We introduce an inhomogeneous term,
f
(
t
,
x
), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions
f
(
t
,
x
) which depend nontrivially on both
t
and
x
, we find that there is just one symmetry. If
f
is a function of only
x
, there are three symmetries with the algebra
s
l
(2,
R
). When
f
is a function of only
t
, there are five symmetries with the algebra
s
l
(2,
R
) ⊕
s
2
A
1
. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.</abstract><cop>New Delhi</cop><pub>Springer India</pub><doi>10.1007/s12043-017-1382-3</doi><tpages>6</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0304-4289 |
| ispartof | Pramāṇa, 2017-05, Vol.88 (5), p.1-6, Article 74 |
| issn | 0304-4289 0973-7111 |
| language | eng |
| recordid | cdi_proquest_journals_1885268137 |
| source | SpringerNature Journals; Indian Academy of Sciences |
| subjects | Algebra Astronomy Astrophysics and Astroparticles Burgers equation Linear equations Mathematical analysis Observations and Techniques Physics Physics and Astronomy Symmetry |
| title | Algebraic resolution of the Burgers equation with a forcing term |
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