The determinant representation of an N-fold Darboux transformation for the short pulse equation

作者：Liu, Shuzhi; Wang, Lihong; Liu, Wei; Qiu, Deqin; He, Jingsong^*

来源：Journal of Nonlinear Mathematical Physics, 2017, 24(2): 183-194.

DOI：10.1080/14029251.2017.1306947

• Darboux transformation
• short pulse equation
• soliton
• hodograph transformation

We present an explicit representation of an N-fold Darboux transformation (T) over tilde (N) for the short pulse equation, by the determinants of the eigenfunctions of its Lax pair. In the course of the derivation of (T) over tilde (N), we show that the quasi-determinant is avoidable, and it is contrast to a recent paper (J. Phys. Soc. Jpn. 81 (2012), 094008) by using this relatively new tool which was introduced to study noncommutative mathematical objectives. (T) over tilde (N) produces new solutions u([N]) and x([N]) which are expressed by ratios of two corresponding determinants. We also obtain the soliton solutions, which have a variable trajectory, of the short pulse equation from new "seed" solutions.

• 出版日期2017
• 单位吉首大学; 宁波大学