2016/05/29 by Jen-Hsu Chang, Chang, Jen-Hsu
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.1605.08966
17 pages
openalex publication_date 2016/05/29 · arxiv created 2017/07/09 · arxiv updated 2017/07/11 · openalex created_date 2017/07/21 · openalex updated_date 2026/07/28
Inspired by the works of Y. Ohta and J. Yang, one constructs the lumps solutions in the Kadomtsev-Petviashvili-(I) equation using the Grammian determinants. It is shown that the locations of peaks will depend on the real roots of Wronskian of the orthogonal polynomials for the asymptotic behaviors in some particular cases. Also, one can prove that all the locations of peaks are on a vertical line when time approaches - ∞, and then they will be on a horizontal line when time approaches ∞, i.e., there is a rotation \fracπ2 after interaction.