Aristophanes Dimakis, Folkert Müller-Hoissen, “Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System”, SIGMA, 2009, том 5,002, 18 стр.

Эта публикация цитируется в 3 статьях

Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System

Aristophanes Dimakis^a, Folkert Müller-Hoissen^b

^a Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Str., GR-82100 Chios, Greece
^b Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073 Göttingen, Germany

Аннотация: Via a Cole–Hopf transformation, the multicomponent linear heat hierarchy leads to a multicomponent Burgers hierarchy. We show in particular that any solution of the latter also solves a corresponding multicomponent (potential) KP hierarchy. A generalization of the Cole–Hopf transformation leads to a more general relation between the multicomponent linear heat hierarchy and the multicomponent KP hierarchy. From this results a construction of exact solutions of the latter via a matrix linear system.

Ключевые слова: multicomponent KP hierarchy; Burgers hierarchy; Cole–Hopf transformation; Davey–Stewartson equation; Riccati equation; dromion.

MSC: 37K10; 35Q53

Поступила: 1 ноября 2008 г.; в окончательном варианте 4 января 2009 г.; опубликована 8 января 2009 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2009.002