Quantum Sine(h)-Gordon Model and Classical Integrable Equations

S. L. Lukyanov, A. B. Zamolodchikov

We study a family of classical solutions of modified sinh-Gordon equation, $\partial_z\partial_{\bar z} η-\re^{2η}+p(z)\,p({\bar z})\ \re^{-2η}=0$ with $p(z)=z^{2\alpha }-s^{2\alpha }$. We sho…