Abstract
SynopsisIn this paper we apply the Painlevé tests to the damped, driven nonlinear Schrödinger equationwhere a(x, t) and b(x, t) are analytic functions of x and t, todetermine under what conditions the equation might be completely integrable. It is shown that (0.1) can pass the Painlevé tests only ifwhere α0(t),α1(t) and β(t) are arbitrary, real analytic functions of time. Furthermore, it is shown that in this special case, (0.1) may be transformed into the original nonlinear Schrödinger equation, which is known to be completely integrable.
Publisher
Cambridge University Press (CUP)
Reference33 articles.
1. Extension of inverse scattering method to nonlinear evolution equation in nonuniform medium
2. Two-dimensional self-modulation of lower hybrid waves in inhomogeneous plasmas
3. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media;Zakharov;Soviet Phys. IETP,1972
4. The inverse scattering transform: Semi‐infinite interval
5. Perturbation theory for solitons and solitary waves;Karpman;Soviet Phys. JETP,1978
Cited by
65 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献