Hynek Baran and Michal Marvan 2009 J. Phys. A: Math. Theor. 42 404007 doi:10.1088/1751-8113/42/40/404007
On integrability of Weingarten surfaces: a forgotten class
Hynek Baran and Michal Marvan
Show affiliationsRediscovered by a systematic search, a forgotten class of integrable surfaces is shown to disprove the Finkel–Wu conjecture. The associated integrable nonlinear partial differential equation 
possesses a zero curvature representation, a third-order symmetry and a nonlocal transformation to the sine-Gordon equation 
ξη = sin . We leave open the problem of finding a Bäcklund autotransformation and a recursion operator that would produce a local hierarchy.
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Issue 40 (9 October 2009)
Received 30 January 2009, in final form 26 May 2009
Published 16 September 2009
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On integrability of Weingarten surfaces: a forgotten class
Hynek Baran and Michal Marvan 2009 J. Phys. A: Math. Theor. 42 404007
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