Modified Korteweg-de Vries Hierarchy Research Articles

Isospectral transformations in relativistic and nonrelativistic mechanics

The modified Korteweg de-Vries hierarchy of partial differential equations generating transformations of the one-dimensional Dirac equation, is shown to reduce in the limitc→∞ to the Korteweg de-Vries hierarchy, generating isospectral transformations of the Schrodinger equation. The former hierarchy reduces into relativistic and the latter into nonrelativistic isoperiodic transformation in the limitħ→0.

On reciprocal auto-Bäcklund transformations: Application to a new nonlinear hierarchy

A hierarchy of nonlinear evolution equations based on the IKW nonlinear oscillation equation is shown to be invariant under a reciprocal Backlund transformation. This result is seen to be a consequence of a simple invariance of the modified Korteweg-deVries hierarchy.