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Dispersion managed solitons in the presence of saturated nonlinearity
Hundertmark, D.,Lee, Y.R.,Ried, T.,Zharnitsky, V. North-Holland 2017 Physica. D, Nonlinear phenomena Vol.356 No.-
The averaged dispersion managed nonlinear Schrodinger equation with saturated nonlinearity is considered. It is shown that under rather general assumptions on the saturated nonlinearity, the ground state solution corresponding to the dispersion managed soliton can be found for both zero residual dispersion and positive residual dispersion. The same applies to diffraction management solitons, which are a discrete version describing certain waveguide arrays.
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>