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Zbl 0755.35121
Rabelo, Mauro L.; Tenenblat, Keti
A classification of pseudospherical surface equations of type $u\sb t=u\sb{xxx}+G(u,u\sb x,u\sb{xx}$).
(English)
[J] J. Math. Phys. 33, No.2, 537-549 (1992). ISSN 0022-2488; ISSN 1089-7658/e

Summary: The equations of type $u\sb t=u\sb{xxx}+G(u,u\sb x,u\sb{xx})$ which describe $\eta$-pseudospherical surfaces are characterized. A new class of such equations is obtained. This class together with the Korteweg-de Vries (KdV) equation, the modified Korteweg-de Vries (MKdV) equation, and the linear equation completes the classification.
MSC 2000:
*35Q53 KdV-like equations

Keywords: modified Korteweg-de Vries equation

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