English

The unified method for the three-wave equation on the half-line

Exactly Solvable and Integrable Systems 2013-04-30 v2

Abstract

We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the three-wave equation: pij,tbibjaiajpij,x+k(bkbjakajbibkaiak)pikpkj=0,i,j,k=1,2,3.p_{ij,t}-\frac{b_i-b_j}{a_i-a_j}p_{ij,x}+\sum_k(\frac{b_k-b_j}{a_k-a_j}-\frac{b_i-b_k}{a_i-a_k})p_{ik}p_{kj}=0,\quad i,j,k=1,2,3. on the half-line.

Keywords

Cite

@article{arxiv.1304.4339,
  title  = {The unified method for the three-wave equation on the half-line},
  author = {Jian Xu and Engui Fan},
  journal= {arXiv preprint arXiv:1304.4339},
  year   = {2013}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1108.2875 by other authors

R2 v1 2026-06-22T00:00:18.503Z