TY - JOUR A2 - Weder, Ricardo AU - Samet, H. Chachou AU - Benarous, M. AU - Asad-uz-zaman, M. AU - Al Khawaja, U. PY - 2014 DA - 2014/09/15 TI - Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity SP - 323591 VL - 2014 AB - We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation. We establish the integrability condition for the most general nonlinear Schrödinger equation with cubic nonlinearity and discuss the effect of the coefficients of the higher-order terms in the solitonic solution. We find that the third-order dispersion term can be used to control the soliton motion without the need for an external potential. We discuss the integrability conditions and find the solitonic solution of some of the well-known nonlinear Schrödinger equations with cubic nonlinearity and time-dependent coefficients. We also investigate the higher-order nonlinear Schrödinger equation with cubic and quintic nonlinearities. SN - 1687-9120 UR - https://doi.org/10.1155/2014/323591 DO - 10.1155/2014/323591 JF - Advances in Mathematical Physics PB - Hindawi Publishing Corporation KW - ER -