Premium
Geometric Formulation and Multi‐dark Soliton Solution to the Defocusing Complex Short Pulse Equation
Author(s) -
Feng BaoFeng,
Maruno KenIchi,
Ohta Yasuhiro
Publication year - 2017
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12159
Subject(s) - hodograph , mathematics , soliton , minkowski space , mathematical analysis , pulse (music) , transformation (genetics) , space (punctuation) , plane (geometry) , nonlinear system , geometry , physics , optics , quantum mechanics , biochemistry , chemistry , linguistics , philosophy , detector , gene
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 R 2 , 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.