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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| Main Author: | |
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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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |