Monodromy deformation approach to nonlinear equations -a survey

Monodromy deformation approach to nonlinear partial differential equation is discussed in a pedestrian's way. The whole methodology is discussed on the basis of Massive Thirring Model. In the first section of our paper we discuss the basic terminologies associated with the deformation problem. In the next part the problem is defined on the basis of the Lax pairs for the Thirring model, and it is explicitly demonstrated that how one can determine the asymptotic expansions near a regular and irregular singularity, and hence the Stokes multipliers. Thirdly we show how to determine the 'third' equation in according to its. In the determination of the asymptotic expansion we have discussed the role played by both the WKB approximation and the series solution. In the fourth section we briefly consider the problem when the nonlinear field variables are taken to be fermionic. (author)