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Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities
Hundertmark, Dirk,Lee, Young-Ran,Ried, Tobias,Zharnitsky, Vadim Elsevier 2018 Journal of differential equations Vol.265 No.8
<P><B>Abstract</B></P> <P>A nonlinear Schrödinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises naturally in modeling fiber-optics communication systems with periodically varying dispersion profile (dispersion management). The associated constrained variational principle is shown to posses a ground state solution by constructing a convergent minimizing sequence through the application of a method similar to the classical concentration compactness principle of Lions. One of the obstacles in applying this variational approach is that a saturated nonlocal nonlinearity does not satisfy uniformly the so-called strict sub-additivity condition. This is overcome by applying a special version of Ekeland's variational principle.</P>
On Dispersion Managed Solitons
Dirk Hundertmark,Young-Ran Lee 한국산업응용수학회 2008 한국산업응용수학회 학술대회 논문집 Vol.4 No.3
We give a brief survey on dispersion managed non-linear Schrodinger equation which is used in fiber optics communications.