Complex coupled dispersionless equations in Minkowski 3-space

ABSTRACT

In this study, we investigate the geometric and algebraic aspects of defocusing Complex Coupled Dispersionless (CCD) equations in Minkowski space. We give the conditions for obtaining CCD equations from moving spacelike or timelike space curves using the Frenet and Darboux frames. Besides, we present the Lax pairs that indicate that the corresponding CCD equations are integrable. Finally, we evaluate the conserved quantities for CCD equations from the geometric point of view.

KEYWORDS:

• Darboux frame
• complex coupled dispersionless equations
• Lax pairs
• conserved quantity
• non-null curves

AMS SUBJECT CLASSIFICATIONS:

• 35Q53
• 35C08
• 53B30

Disclosure statement

No potential conflict of interest was reported by the author(s).