caa a22 4500 47583965X CHVBK 20180406123858.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1010774630016 doi (NATIONALLICENCE)springer-10.1023/A:1010774630016 Reyes Enrique Department of Mathematics and Statistics, Utah State University, 84322-3900, Logan, UT, U.S.A. aut Some Geometric Aspects of Integrability of Differential Equations in Two Independent Variables [Elektronische Daten] [Enrique Reyes] The relation between scalar evolution equations which are the integrability condition of sl(2,R)-valued linear problems with parameter (‘kinematic' integrability) and those which possess recursion operators (‘formal' integrability) is studied: using that kinematically integrable equations describe one-parameter families of pseudo-spherical surfaces and vice versa, it is shown that every second order formally integrable evolution equation is kinematically integrable, and that this result cannot be extended as proven to the third-order case. Conservation laws of kinematically integrable equations obtained from their underlying pseudo-spherical structure are compared with the ones one finds from the ‘Riccati equation' version of their associated linear problems. Symmetries (generalized/nonlocal) for these equations are also studied, by considering infinitesimal deformations of the associated pseudo-spherical surfaces. Finally, conservation laws for equations describing pseudo-spherical surfaces immersed in a flat three-space are found, and the class of ‘equations describing Calapso-Guichard surfaces' is introduced. Kluwer Academic Publishers, 2000 pseudo-spherical surfaces nationallicence Calapso-Guichard surfaces nationallicence kinematic integrability nationallicence geometric integrability nationallicence formal integrability nationallicence symmetries nationallicence conservation laws nationallicence Acta Applicandae Mathematica Kluwer Academic Publishers 64/2-3(2000-11-01), 75-109 0167-8019 64:2-3<75 2000 64 10440 https://doi.org/10.1023/A:1010774630016 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1010774630016 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Reyes Enrique Department of Mathematics and Statistics, Utah State University, 84322-3900, Logan, UT, U.S.A aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 64/2-3(2000-11-01), 75-109 0167-8019 64:2-3<75 2000 64 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer