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From the Real and Complex Coupled Dispersionless Equations to the Real and Complex Short Pulse Equations
Author(s) -
Shen Shoufeng,
Feng BaoFeng,
Ohta Yasuhiro
Publication year - 2016
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.12092
Subject(s) - hodograph , mathematics , hierarchy , connection (principal bundle) , real line , pulse (music) , product (mathematics) , system of linear equations , mathematical analysis , soliton , nonlinear system , pure mathematics , physics , geometry , quantum mechanics , voltage , economics , market economy
In the present paper, we study the real and complex coupled dispersionless (CD) equations, the real and complex short pulse (SP) equations geometrically and algebraically. From the geometric point of view, we first establish the link of the motions of space curves to the real and complex CD equations, then to the real and complex SP equations via hodograph transformations. The integrability of these equations are confirmed by constructing their Lax pairs geometrically. In the second part of the paper, it is made clear for the connection between the real and complex CD and SP equations and the two‐component extended Kadomtsew‐Petviashvili (KP) hierarchy. As a by‐product, the N ‐soliton solutions in the form of determinants for these equations are provided.