### Abstract

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 language | English |
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Journal | Studies in Applied Mathematics |

DOIs | |

Publication status | Accepted/In press - 2016 |

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### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Studies in Applied Mathematics*. https://doi.org/10.1111/sapm.12159

**Geometric Formulation and Multi-dark Soliton Solution to the Defocusing Complex Short Pulse Equation.** / Feng, Bao Feng; Maruno, Kenichi; Ohta, Yasuhiro.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Geometric Formulation and Multi-dark Soliton Solution to the Defocusing Complex Short Pulse Equation

AU - Feng, Bao Feng

AU - Maruno, Kenichi

AU - Ohta, Yasuhiro

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85007165354&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007165354&partnerID=8YFLogxK

U2 - 10.1111/sapm.12159

DO - 10.1111/sapm.12159

M3 - Article

AN - SCOPUS:85007165354

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

ER -