Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy

2014/09/30 by Oleksandr Chvartatskyi, Yuriy Sydorenko · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Arithmetic #Binary number #Darboux integral #Geometry #Hierarchy #Integrable system #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pure mathematics #msc:35Q51 #msc:35Q53 #msc:35Q55 #msc:37K35 #nlin.SI

paper · pdf · doi:10.3842/sigma.2015.028

published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)

arxiv created 2015/04/10 · openalex publication_date 2015/04/10 · arxiv updated 2015/04/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of (2+1)-dimensional integrable equations, including the DS-III equation and the N -wave problem. Furthermore, we recover a system that contains two types of the KP equation with self-consistent sources as special cases. Darboux and binary Darboux transformations are applied to generate solutions of the proposed hierarchies.

Citations

• An algebraic scheme associated with the non-commutative KP hierarchy and some of its extensions
• Towards noncommutative integrable systems
• A new extended KP hierarchy
• Dispersionful analogues of Benney's equations and N -wave systems
• Solutions of matrix NLS systems and their discretisations: A unified treatment