Explicit formulas for spectral characteristics and solutions of the sh- Gordon equation (Q1174067)

The paper considers the sh-Gordon equation \(\partial^ 2\varphi/\partial t\partial x = 4 sh \varphi\), \(0\leq x\), \(t<\infty\), to which the linear system \(\partial w/\partial x=izH(x,t)w\), \(w(0,t,z)\in E_{2}\) corresponds. Denoting by \(v(t,z)\) the Weyl-Titchmarsh function of the above system, the author studies the case where \(v\) is a rational function. In this case \(v\) can be found explicitly; as a consequence the function \(\varphi\) can be given explicitly.