Abstract
The Fokas method is used to analyze the initial–boundary value problem for the three-wave equationpij,t−bi−bjai−ajpij,x+∑k(bk−bjak−aj−bi−bkai−ak)pikpkj=0,i,j,k=1,2,3, on the half-line. Assuming that the solution pij(x,t) exists, we show that it can be recovered from its initial and boundary values via the solution of a Riemann–Hilbert problem formulated in the plane of the complex spectral parameter λ.
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