Geometric Formulation and Multi-dark Soliton Solution to the Defocusing Complex Short Pulse Equation

Bao Feng Feng, Ken Ichi Maruno, Yasuhiro Ohta

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6 Citations (Scopus)


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 defocusing CSP equation from the single-component extended Kadomtsev-Petviashvili (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.

Original languageEnglish
Pages (from-to)343-367
Number of pages25
JournalStudies in Applied Mathematics
Issue number3
Publication statusPublished - 2017 Apr 1


ASJC Scopus subject areas

  • Applied Mathematics

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