THE mKdV EQUATION ON THE HALF-LINE

An initial boundary-value problem for the modified Korteweg–de Vries equation on the half-line, . It is shown that for a particular class of boundary conditions, the linearizable boundary conditions, all the spectral functions can be computed from the given initial data by using algebraic manipulations of the global relation; thus, in this case, the problem on the half-line can be solved as efficiently as the problem on the whole line.AMS 2000 Mathematics subject classification: Primary 37K15; 35Q53. Secondary 35Q15; 34A55