کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4624052 | 1339530 | 2006 | 14 صفحه PDF | دانلود رایگان |

Zero dispersion and viscosity limits of invariant manifolds for focusing nonlinear Schrödinger equations (NLS) are studied. We start with spatially uniform and temporally periodic solutions (the so-called Stokes waves). We find that the spectra of the linear NLS at the Stokes waves often have surprising limits as dispersion or viscosity tends to zero. When dispersion (or viscosity) is set to zero, the size of invariant manifolds and/or Fenichel fibers approaches zero as viscosity (or dispersion) tends to zero. When dispersion (or viscosity) is nonzero, the size of invariant manifolds and/or Fenichel fibers approaches a nonzero limit as viscosity (or dispersion) tends to zero. When dispersion is nonzero, the center-stable manifold, as a function of viscosity, is not smooth at zero viscosity. A subset of the center-stable manifold is smooth at zero viscosity. The unstable Fenichel fiber is smooth at zero viscosity. When viscosity is nonzero, the stable Fenichel fiber is smooth at zero dispersion.
Journal: Journal of Mathematical Analysis and Applications - Volume 315, Issue 2, 15 March 2006, Pages 642-655