Stability of multi-solitons in the cubic NLS equation

preprint2013arXivOpen access

We address stability of multi-solitons in the cubic NLS (nonlinear Schrödinger) equation on the line. By using the dressing transformation and the inverse scattering transform methods, we obtain the orbital stability of multi-solitons in the $L^2(\mathbb{R})$ space when the initial data is in a weighted $L^2(\mathbb{R})$ space.

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Stability of multi-solitons in the cubic NLS equation

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