Quasi-continuum approximation to the Nonlinear Schrödinger equation with Long-range dispersions

Details Quasi-continuum approximation to the Nonlinear Schrödinger equation with Long-range dispersions Quasi-continuum approximation to the Nonlinear Schrödinger equation with Long-range dispersions

2004-02-13

arxiv.org/abs/nlin/0402020v1

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

The long-wavelength, weak-dispersion limit of the discrete nonlinear Schr\"odinger equation with long-range dispersion is analytically considered. This continuum approximation is carried out irrespective of the dispersion range and hence can be assumed exact in the weak dispersion regime. For nonlinear Schr\"odinger equations showing finite dispersion extents, the long-range parameter is still a relevant control parameter allowing to tune the dispersion from short-range to long-range regimes with respect to the dispersion extent. The long-range Kac-Baker potential becomes unappropriate in this context owing to an "edge anomaly" consisting of vanishing maximum dispersion frequency and group velocity(and in turn soliton width) in the "Debye" limit. An improved Kac-Baker potential is then considered which gives rise to a non-zero maximum frequency, and allows for soliton excitations with finite widths in the nonlinear Schr\"odinger system subjected to the long-range but finite-extent dispersion.

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