A systematic method is developed of constructing the model associated with any given nonlinear evolution equation solvable by the inverse scattering method. The model is obtained from the adjoint representation of the group associated with the Lax representation of the evolution equation. Bäcklund transformations for the model and for the evolution equation are realized as gauge transformations. The complete integrability of the model follows from Pohlmeyer's R transformation which is systematically constructed in each case. The examples of the sine-Gordon, nonlinear Schrödinger, Korteweg-de Vries, and modified Korteweg-de Vries equations are discussed in detail.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)