2006/12/31 by A. I. Zenchuk
Mathematics · Physics and Astronomy · #Differential equation #Dimension (graph theory) #First-order partial differential equation #Fractional Differential Equations Solutions #Generalization #Integrable system #Integral equation #Nonlinear Waves and Solitons #Numerical methods for differential equations #Partial differential equation #Polynomial #nlin.SI
paper · pdf · doi:10.1063/1.2759444
published in Journal of Mathematical Physics 48(8) (American Institute of Physics) · 38 pages
arxiv created 2007/07/13 · openalex publication_date 2007/08/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This paper develops a modification of the dressing method based on the inhomogeneous linear integral equation with integral operator having nonempty kernel. The method allows one to construct the systems of multidimensional partial differential equations having differential polynomial structure in any dimension n. The associated solution space is not full, although it is parametrized by certain number of arbitrary functions of (n−1) variables. We consider four-dimensional generalization of the classical (2+1)-dimensional S-integrable N-wave equation as an example.