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- Title
Cauchy matrix approach to the noncommutative Kadomtsev–Petviashvili equation with self-consistent sources.
- Authors
Shi, Zhihao; Li, Shangshuai; Zhang, Da-jun
- Abstract
We develop a direct method, the Cauchy matrix approach, to construct matrix solutions of noncommutative soliton equations. This approach is based on the Sylvester equation, and solutions can be presented without using quasideterminants. The matrix Kadomtsev–Petviashvili equation with self-consistent sources is employed as an example to demonstrate the approach. As a reduction, explicit solutions of the matrix Mel'nikov model for long–short wave interaction are obtained.
- Subjects
KADOMTSEV-Petviashvili equation; SYLVESTER matrix equations
- Publication
Theoretical & Mathematical Physics, 2022, Vol 213, Issue 3, p1686
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1134/S0040577922120030