Higher-order rogue wave solutions of the Sasa–Satsuma equation

• Published in: Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2022-05, Vol.55 (23), p.235701
• Main Authors: Feng, Bao-Feng, Shi, Changyan, Zhang, Guangxiong, Wu, Chengfa
• Format: Article
• Language: English
• Subjects: Kadomtsev–Petviashvili hierarchy reduction method; rogue wave; Sasa–Satsuma equation
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8121/ac6917

Up to the third-order rogue wave solutions of the Sasa–Satsuma (SS) equation are derived based on the Hirota’s bilinear method and Kadomtsev–Petviashvili hierarchy reduction method. They are expressed explicitly by rational functions with both the numerator and denominator being the determinants of even order. Four types of intrinsic structures are recognized according to the number of zero-amplitude points. The first- and second-order rogue wave solutions agree with the solutions obtained so far by the Darboux transformation. In spite of the very complicated solution form compared with the ones of many other integrable equations, the third-order rogue waves exhibit two configurations: either a triangle or a distorted pentagon. Both the types and configurations of the third-order rogue waves are determined by different choices of free parameters. As the nonlinear Schrödinger equation is a limiting case of the SS equation, it is shown that the degeneration of the first-order rogue wave of the SS equation converges to the Peregrine soliton.