%0 Journal Article %1 Ilg2016 %A Ilg, Tobias %A Tschüter, Ramona %A Junginger, Andrej %A Main, Jörg %A Wunner, Günter %D 2016 %J The European Physical Journal D %K main_itp1 %N 11 %P 232 %R 10.1140/epjd/e2016-70338-7 %T Dynamics of solitons in the one-dimensional nonlinearSchrödinger equation %U https://doi.org/10.1140/epjd/e2016-70338-7 %V 70 %X We investigate bright solitons in the one-dimensional Schrödinger equation in theframework of an extended variational approach. We apply the latter to the stationaryground state of the system as well as to coherent collisions between two or more solitons.Using coupled Gaussian trial wave functions, we demonstrate that the variational approachis a powerful method to calculate the soliton dynamics. This method has the advantage thatit is computationally faster compared to numerically exact grid calculations. In addition,it goes far beyond the capability of analytical ground state solutions, because thevariational approach provides the ability to treat excited solitons as well as dynamicalinteractions between different wave packets. To demonstrate the power of the variationalapproach, we calculate the stationary ground state of the soliton and compare it with theanalytical solution showing the convergence to the exact solution. Furthermore, we extendour calculations to nonstationary solitons by investigating coherent collisions of severalwave packets in both the low- and high-energy regime. Comparisons of the variationalapproach with numerically exact simulations on grids reveal excellent agreement in thehigh-energy regime while deviations can be observed for low energies.

@article{Ilg2016, abstract = {We investigate bright solitons in the one-dimensional Schr{\"o}dinger equation in theframework of an extended variational approach. We apply the latter to the stationaryground state of the system as well as to coherent collisions between two or more solitons.Using coupled Gaussian trial wave functions, we demonstrate that the variational approachis a powerful method to calculate the soliton dynamics. This method has the advantage thatit is computationally faster compared to numerically exact grid calculations. In addition,it goes far beyond the capability of analytical ground state solutions, because thevariational approach provides the ability to treat excited solitons as well as dynamicalinteractions between different wave packets. To demonstrate the power of the variationalapproach, we calculate the stationary ground state of the soliton and compare it with theanalytical solution showing the convergence to the exact solution. Furthermore, we extendour calculations to nonstationary solitons by investigating coherent collisions of severalwave packets in both the low- and high-energy regime. Comparisons of the variationalapproach with numerically exact simulations on grids reveal excellent agreement in thehigh-energy regime while deviations can be observed for low energies.}, added-at = {2018-12-04T23:33:10.000+0100}, author = {Ilg, Tobias and Tsch{\"u}ter, Ramona and Junginger, Andrej and Main, J{\"o}rg and Wunner, G{\"u}nter}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2161f903edf1dfe1d32eb9f7bece07dbd/rbardak}, day = 03, description = {Dynamics of solitons in the one-dimensional nonlinear Schrödinger equation | SpringerLink}, doi = {10.1140/epjd/e2016-70338-7}, interhash = {b120867a7a9892ef474ce27efa3d45f2}, intrahash = {161f903edf1dfe1d32eb9f7bece07dbd}, issn = {1434-6079}, journal = {The European Physical Journal D}, keywords = {main_itp1}, month = nov, number = 11, pages = 232, timestamp = {2018-12-04T22:33:10.000+0100}, title = {Dynamics of solitons in the one-dimensional nonlinearSchr{\"o}dinger equation}, url = {https://doi.org/10.1140/epjd/e2016-70338-7}, volume = 70, year = 2016 }