# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Intrinsic formulation of geometric integrability and associated Riccati system generating conservation laws. (English) Zbl 1188.53090

The aim of the paper is to study, firstly, the formulation of Bäcklund transformations based on a Pfaffian system for the case of nonlinear evolution equations which describe pseudospherical surfaces, this is, surfaces with negative constant Gauss curvature, and secondly the determination of conservation laws for such equations.

Starting from the structure equations of a surface with Gauss curvature equal to $-1$, the author is able to transform them into an associated system of differential equations in a Riccati form and to formulate the equivalent linear problem. All this has been done in an intrinsic way.

Finally, it is shown that geometrical properties of a pseudospherical surface provide a systematic method for obtaining an infinite number of conservation laws.

##### MSC:
 53C80 Applications of global differential geometry to physics 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions (global) 35Q53 KdV-like (Korteweg-de Vries) equations 53A10 Minimal surfaces, surfaces with prescribed mean curvature