Analytic solutions to nonelliptic nonlinear Schrödinger equations (Q687505)

This paper proves the existence of solutions holomorphic in the space variables, defined for small times, for a general class of equations including the Boussinesq equation and more sophisticated water-wave model equations (some of them involving a Hilbert transform) due to Dysthe and Hogan. The solutions are analytic in a strip which, in general, may shrink to zero width in finite time. These results generalize two papers of \textit{N. Hayashi} [SIAM J. Math. Anal. 22, No. 6, 1738--1743 (1991; Zbl 0742.35056) and Duke Math. J. 60, No. 3, 717--727 (1990; Zbl 0721.35026)] and the proofs involve similar techniques.