Abstract
A Lie algebra which consists of linear combinations of one basis of the Lie algebra A1 is presented for which an isospectral Lax pair is exhibited. By using the zero curvature equation, the generalized mKdV equation, Liouville equation and sine-Gordon equation, sinh-Gordon equation are generated via polynomial expansions. Finally, we investigate a kind of formal Bäcklund transformation for the generalized sine-Gordon equation. The explicit Bäcklund transformation of the standard sine-Gordon equation is presented. The other equations given in the paper are obtained similarly.
Original language | English |
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Pages (from-to) | 2449-2460 |
Number of pages | 12 |
Journal | International Journal of Modern Physics B |
Volume | 25 |
Issue number | 18 |
DOIs | |
Publication status | Published - 20 Jul 2011 |
User-Defined Keywords
- Bäcklund transformation
- Lie algebra
- Liouville equation
- mKdV equation
- sine-Gordon equation
- sinh-Gordon equation