부산대학교 도서관

The time flow of the periodic Sine-Gordon equation, q/sub tt/ - q/sub xx/ + sin q = 0 fixes the periodic and antiperiodic spectrum of a certain differential operator Q with periodic coefficients (q,p) where p = q/sub t/. The isospectral class L(q/sub 0/,p/sub 0/) consisting of all coefficients (q,p) with the same periodic and antiperiodic spectrum as a given coefficient (q/sub 0/,p/sub 0/) is studied in detail. Compactness and regularity results for L(q/sub 0/,p/sub 0/) are proven by means of various eigenfunction identities. An example is given which shows that L(q/sub 0/,p/sub 0/) need not be connected and another example is given which shows that L(q/sub 0/,p/sub 0/) may have singularities. A particle system is developed which reduces the inverse problem to solution of a differential equation. This thesis extends the work of McKean and Trubowitz on Hill's equation to the sine-Gordon equation.