On the Coupled Dispersionless-type Equations and the Short Pulse-type Equations
- 10.2991/jnmp.k.200922.002How to use a DOI?
- Short pulse equation; coupled integrable dispersionless equations; sine-Gordon equation; AKNS
In this paper, we study the correspondence between the Coupled Dispersionless (CD)-type equations and the Short Pulse (SP)-type equations. From the real and complex modified CD equations, we construct the real and complex Modified Short Pulse (mSP) equations geometrically and algebraically. From the geometric point of view, we establish the link of the motions of space curves to the real and complex modified CD equations, then to the real and complex mSP equations via hodograph transformations. The integrability of these equations are confirmed by constructing their Lax pairs geometrically. By using hodograph transformation, we construct the two-component SP equation from the CD-type equations, the multi-component real and complex SP and mSP equations from the multi-component CD equations. The multi-soliton solutions in the determinant form for the mSP and two-component SP equations are provided.
- © 2020 The Authors. Published by Atlantis Press B.V.
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Juan Hu AU - Jia-Liang Ji AU - Guo-Fu Yu PY - 2020 DA - 2020/12/10 TI - On the Coupled Dispersionless-type Equations and the Short Pulse-type Equations JO - Journal of Nonlinear Mathematical Physics SP - 14 EP - 26 VL - 28 IS - 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.k.200922.002 DO - 10.2991/jnmp.k.200922.002 ID - Hu2020 ER -