Details

Autor(en) / Beteiligte

• Xu, Jian
• Fan, Engui

Titel

The three-wave equation on the half-line

Ist Teil von

• Physics letters. A, 2014-01, Vol.378 (1-2), p.26-33

Ort / Verlag

Elsevier B.V

Erscheinungsjahr

2014

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• •We present a Riemann–Hilbert problem formalism for the initial–boundary value problem of the three-wave equation.•The residue conditions of matrix function M in the Riemann–Hilbert problem is obtained.•The explicit jump matrix J in the Riemann–Hilbert problem is constructed. 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.