On the Relations among Nonlinear PDEs with Different Integrability Properties: C-S-,Ch-C- and Ch-S-integrable systems, pp. 605-619
Authors: (A.I. Zenchuk, Institute of Problems of Chemical Physics RAS, Chernogolovka, Moscow Region, Russia)
Abstract: Remarkable relations among nonlinear Partial Differential Equations (PDEs) integrable by the Hopf-Cole substitution, by the method of characteristics and by the Inverse Spectral Transform Method (ISTM) have been established recently. These relations exist due to the fact that matrix fields (dependent variables) of both PDEs linearizable by Hoph-Cole substitution and PDEs integrable by the method of characteristics admit the Frobenious structure. This paper is devoted to generalization of this algorithm in order to involve PDEs having more complicated integration algorithm. Namely, nonlinear equations having properties of both PDEs (a) linearizable and integrable by the ISTM, (b) linearizable and integrable by the method of characteristics,(b) integrable by the method of characteristics and Self-dual type PDEs integrable by the ISTM.