Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions
The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invariant solutions for it are obtained by means of this technique. Polynomial, trigonometric, and elliptic function solutions can be calculated. It is shown that this generalized equation c...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2159 |
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| _version_ | 1832549817550635008 |
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| author | Paul Bracken |
| author_facet | Paul Bracken |
| author_sort | Paul Bracken |
| collection | DOAJ |
| description | The symmetry group method is applied to a generalized Korteweg-de
Vries equation and several classes of group invariant solutions
for it are obtained by means of this technique. Polynomial,
trigonometric, and elliptic function solutions can be calculated.
It is shown that this generalized equation can be reduced to a
first-order equation under a particular second-order differential
constraint which resembles a Schrödinger equation. For a
particular instance in which the constraint is satisfied, the
generalized equation is reduced to a quadrature. A condition which
ensures that the reciprocal of a solution is also a solution is
given, and a first integral to this constraint is found. |
| format | Article |
| id | doaj-art-b2d64bd884c64c73990708fd4937eb17 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b2d64bd884c64c73990708fd4937eb172025-02-03T06:08:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005132159217310.1155/IJMMS.2005.2159Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutionsPaul Bracken0Department of Mathematics, University of Texas-Pan American, Edinburg 78539-2999, TX, USAThe symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invariant solutions for it are obtained by means of this technique. Polynomial, trigonometric, and elliptic function solutions can be calculated. It is shown that this generalized equation can be reduced to a first-order equation under a particular second-order differential constraint which resembles a Schrödinger equation. For a particular instance in which the constraint is satisfied, the generalized equation is reduced to a quadrature. A condition which ensures that the reciprocal of a solution is also a solution is given, and a first integral to this constraint is found.http://dx.doi.org/10.1155/IJMMS.2005.2159 |
| spellingShingle | Paul Bracken Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions International Journal of Mathematics and Mathematical Sciences |
| title | Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions |
| title_full | Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions |
| title_fullStr | Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions |
| title_full_unstemmed | Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions |
| title_short | Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions |
| title_sort | symmetry properties of a generalized korteweg de vries equation and some explicit solutions |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2159 |
| work_keys_str_mv | AT paulbracken symmetrypropertiesofageneralizedkortewegdevriesequationandsomeexplicitsolutions |