This article is cited in 8 papers

An analogue of the Moutard transformation for the Goursat equation $\theta_{xy}=2\sqrt {\lambda(x,y)\theta_x\theta_y}$

E. I. Ganzha

Krasnoyarsk State Pedagogical University named after V. P. Astaf'ev

Abstract: We present a new Bäcklund-type transformation for the nonlinear equation $\theta_{xy}=2\sqrt{\lambda(x,y)\theta_x\theta_y}$ studied by É. Goursat. Goursat found a linearization transformation and some properties of this equation, which make it similar to the Moutard equation $u_{xy}=M(x,y)u$. However, this Goursat transformation does not provide proper superposition formulas. We give the necessary extended superposition formulas.

DOI: 10.4213/tmf554

 English version: Theoretical and Mathematical Physics, 2000, 122:1, 39–45

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