The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schrodinger equation with Kerr nonlinearity and optical lattice.The approximate analytical soliton solutions are obtain...The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schrodinger equation with Kerr nonlinearity and optical lattice.The approximate analytical soliton solutions are obtained based on the variational approach,which provides reasonable accuracy.Linear-stability analysis shows that all the solitons are linearly stable.No collapses are found when the Levy index 1<α≤2.Forα=1,the collapse is arrested by the lattice potential when the amplitude of perturbations is small enough.It is numerically proved that the energy criterion of collapse suppression in the two-dimensional traditional Schrodinger equation still holds in the one-dimensional fractional Schr odinger equation.The physical mechanism for collapse prohibition is also given.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11947122)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515110935)+2 种基金the Research Start-up Foundation of Dongguan University of Technology,the Guangdong Science and Technology Planning Program(Grant No.2017A010102019)the Guangdong Province Natural Science Foundation of China(Grant Nos.2018A030307028 and 2019A1515010916)the Maoming Natural Science Foundation of Guangdong,China(Grant No.2019018001).
文摘The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schrodinger equation with Kerr nonlinearity and optical lattice.The approximate analytical soliton solutions are obtained based on the variational approach,which provides reasonable accuracy.Linear-stability analysis shows that all the solitons are linearly stable.No collapses are found when the Levy index 1<α≤2.Forα=1,the collapse is arrested by the lattice potential when the amplitude of perturbations is small enough.It is numerically proved that the energy criterion of collapse suppression in the two-dimensional traditional Schrodinger equation still holds in the one-dimensional fractional Schr odinger equation.The physical mechanism for collapse prohibition is also given.
