Framed Curve Families Induced by Real and Complex Coupled Dispersionless-Type Equations

Nikola Popović, Kemal Eren (), Ana Savić and Soley Ersoy
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Nikola Popović: Faculty of Mathematics and Computer Science, Alfa BK University, 11000 Belgrade, Serbia
Kemal Eren: Sakarya University Technology Developing Zones Manager Company, 54050 Sakarya, Turkey
Ana Savić: School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, 11000 Belgrade, Serbia
Soley Ersoy: Department of Mathematics, Faculty of Sciences, University of Sakarya, 54050 Sakarya, Turkey

Mathematics, 2023, vol. 11, issue 16, 1-13

Abstract: In this study, we investigate coupled real and complex dispersionless equations for curve families, even if they have singular points. Even though the connections with the differential equations and regular curves were considered in various ways in the past, since each curve does not need to be regular, we establish the connections for framed base curves, which generalize regular curves with linear independent conditions. Also, we give the Lax pairs of the real and complex coupled dispersionless equations from the motions of any framed curve. These give us significant conditions based on the framed curvatures and associated curvatures of the framed curves for integrability since it is well known that the Lax pair provides the integrability of differential equations.

Keywords: complex coupled dispersionless equation; real coupled dispersionless equation; framed curved; Lax pairs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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