On an Explicitly Soluble System of Nonlinear Differential Equations Related to Certain Toda Lattices

Publisher Summary This chapter discusses an explicitly soluble system of nonlinear differential equations related to certain Toda lattices. Toda lattice was solved by applying a discrete version of the inverse scattering problem. By assuming that there are no bound states, one can use formula to determine the spectral function. The solution of the finite system yields also the solution to the finite Toda chain with two free ends, a problem that has been recently solved. If α is chosen sufficiently large, the α and η'S will be positive and hence, their logarithms are real. It is somewhat curious that while the p's and q's are uniquely determined, the R's do not owe to the arbitrariness of α.