2012/08/08 by Tao Xu, Xu, Tao, Fu-Wei Sun +5
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1208.1570
24 pages, 6 figures
arxiv created 2012/08/08 · openalex publication_date 2012/08/08 · arxiv updated 2012/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that the Kadomtsev-Petviashvili (KP) equation can be decomposed into the first two members of the coupled Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy by the binary nonlinearization of Lax pairs. In this paper, we construct the N-th iterated Darboux transformation (DT) for the second- and third-order m-coupled AKNS systems. By using together the N-th iterated DT and Cramer's rule, we find that the KPII equation has the unreduced multi-component Wronskian solution and the KPI equation admits a reduced multi-component Wronskian solution. In particular, based on the unreduced and reduced two-component Wronskians, we obtain two families of fully-resonant line-soliton solutions which contain arbitrary numbers of asymptotic solitons as y->∓∞ to the KPII equation, and the ordinary N-soliton solution to the KPI equation. In addition, we find that the KPI line solitons propagating in parallel can exhibit the bound state at the moment of collision.