2016/03/02 by Bao‐Feng Feng, Feng, Bao-Feng, Ken‐ichi Maruno +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1603.00781
openalex publication_date 2016/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper, we study the defocusing complex short pulse (CSP) equations both geometrically and algebraically. From the geometric point of view, we establish a link of the complex coupled dispersionless (CCD) system with the motion of space curves in Minkowski space R2,1, then with the defocusing CSP equation via a hodograph (reciprocal) transformation, the Lax pair is constructed naturally for the defocusing CSP equation. We also show that the CCD system of both the focusing and defocusing types can be derived from the fundamental forms of surfaces such that their curve flows are formulated. In the second part of the paper, we derive the the defocusing CSP equation from the single-component extended KP hierarchy by the reduction method. As a by-product, the N-dark soliton solution for the defocusing CSP equation in the form of determinants for these equations is provided.