TY - JOUR

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

AU - Feng, Bao Feng

AU - Maruno, Ken Ichi

AU - Ohta, Yasuhiro

N1 - Funding Information:
We thank for the reviewers' comments that helped us to improve the manuscript significantly. BF appreciates the useful discussion on geometric part of the paper with Dr. Zhiwei Wu. The work of BF is partially supported by the National Natural Science Foundation of China (No. 11428102). The work of KM is partially supported by JSPS Grant-in-Aid for Scientific Research (C-15K04909) and CREST, JST. The work of YO is partly supported by JSPS Grant-in-Aid for Scientific Research (B-24340029, C-15K04909) and for Challenging Exploratory Research (26610029).

PY - 2017/4/1

Y1 - 2017/4/1

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.

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U2 - 10.1111/sapm.12159

DO - 10.1111/sapm.12159

M3 - Article

AN - SCOPUS:85007165354

VL - 138

SP - 343

EP - 367

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 3

ER -