Geometry of coupled dispersionless equations by using bishop frames

K. Eren

In this study, we investigate the equations of the coupled dispersionless and complex coupled dispersionless by an alternative point of view to avoid insufficiency occurs for sudden orientation changes when the curve straightens out momentarily by considering a moving coordinate frame on a space curve based on the concept of parallel transport. Firstly, we study the correlation between the type-1 Bishop frame of a space curve and the coupled dispersionless equation: then we discover the correlation between the type-2 Bishop frame and the complex coupled dispersionless equations. Finally, we give the integrability conditions of the obtained differential equations by finding the Lax pair. 

Tbilisi Mathematical Journal, Special Issue (IECMSA-2019), pp. 39-48