Department of Computer Science
Generalized mkdv equation, liouville equation, sine-gordon equation and sinh-gordon equation as well as a formal Bäcklund transformation
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. © 2011 World Scientific Publishing Company.
Bäcklund transformation, Lie algebra, Liouville equation, mKdV equation, sine-Gordon equation, sinh-Gordon equation
Source Publication Title
International Journal of Modern Physics B
World Scientific Publishing
Zhang, Yufeng, Honwah Tam, and Jing Zhao. "Generalized mkdv equation, liouville equation, sine-gordon equation and sinh-gordon equation as well as a formal Bäcklund transformation." International Journal of Modern Physics B 25.18 (2011): 2449-2460.