Higher-order rogue wave solutions of the Sasa–Satsuma equation
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- May 16, 2022
- Source ID
- 10.1088/1751-8121/ac6917
Entities
People
- Bao‐Feng Feng
- Changyan Shi
- Chengfa Wu
- Guangxiong Zhang
Organizations
- National Natural Science Foundation of China
- National Science Foundation
- United States Department of Defense