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

Bao Feng Feng, Kenichi Maruno, Yasuhiro Ohta

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    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 languageEnglish
    JournalStudies in Applied Mathematics
    DOIs
    Publication statusAccepted/In press - 2016

    Fingerprint

    Short Pulse
    Soliton Solution
    Solitons
    Byproducts
    Formulation
    Coupled System
    Complex Systems
    Space Curve
    Lax Pair
    Minkowski Space
    Reduction Method
    Determinant
    Curve
    Motion

    ASJC Scopus subject areas

    • Applied Mathematics

    Cite this

    @article{8ba65757c20a447c8c6eabdb5653319f,
    title = "Geometric Formulation and Multi-dark Soliton Solution to the Defocusing Complex Short Pulse Equation",
    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.",
    author = "Feng, {Bao Feng} and Kenichi Maruno and Yasuhiro Ohta",
    year = "2016",
    doi = "10.1111/sapm.12159",
    language = "English",
    journal = "Studies in Applied Mathematics",
    issn = "0022-2526",
    publisher = "Wiley-Blackwell",

    }

    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

    JO - Studies in Applied Mathematics

    JF - Studies in Applied Mathematics

    SN - 0022-2526

    ER -