An analogue of the Moutard transformation for the Goursat equation $\theta_{xy}=2\sqrt {\lambda(x,y)\theta_x\theta_y}$
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 50-57
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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.
@article{TMF_2000_122_1_a4,
author = {E. I. Ganzha},
title = {An analogue of the {Moutard} transformation for the {Goursat} equation $\theta_{xy}=2\sqrt {\lambda(x,y)\theta_x\theta_y}$},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {50--57},
publisher = {mathdoc},
volume = {122},
number = {1},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a4/}
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E. I. Ganzha. An analogue of the Moutard transformation for the Goursat equation $\theta_{xy}=2\sqrt {\lambda(x,y)\theta_x\theta_y}$. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 50-57. http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a4/