Abstract:
The study of integrable systems or solvable nonlinear differential equations (NDE)
has been an active area of research since the discovery of the inverse scattering method. These
equations are in a sense universal because they are found in many areas of physics and mathematics.
By integrable systems, we mean those that have an infinite hierarchy of symmetries and conservation
laws. There are several parallel construction schemes for the integrated systems. In addition to the
integrable NDE, there is another important class of integrable partial differential equations: the socalled integrable hydrodynamic equations often called dispersionless equations. They often arise in
various physics and mathematics problems and have been intensively studied in recent years. In this
paper we investigate the coupled integrable dispersionless equation and its reduction. The dispersionless (quasiclassical) limit for the Konno-Oono equation is obtained and the Lax representation
is constructed, which proves its integrability.
