Add to ORKGAmong other things, we introduce the notion of KdV curves and Schrodinger-Airy curves. These curves are stable solutions to the geometric KdV-Airy flow equation and Schrodinger-Airy flow equation respectively, which were recently proposed by Sun and Wang. We demonstrate that the KdV curves can be regarded as a 3rd-order analogue of geodesics. Other interesting properties of these curves will be addressed. Explicit examples of these curves will be provided. In addition, we will consider a perturbed KdV curve system and show the existence of multiple solutions to this system on the torus.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000300128300026&DestLinkType=FullRecord&DestA...