Based on the method of Hirota＇s bilinear derivative transform, the derivative nonlinear Schrodinger equation with vanishing boundary condition has been directly solved. The oneand two-soliton solutions are given as t...Based on the method of Hirota＇s bilinear derivative transform, the derivative nonlinear Schrodinger equation with vanishing boundary condition has been directly solved. The oneand two-soliton solutions are given as two typical examples in the illustration of the general procedures and the concrete cut-off technique of the series-form solution, and the n-soliton solution is also attained by induction method. Our study shows their equivalence to the existing soliton solutions by a simple parameter transformation. The methodological importance of bilinear derivative transform in dealing with an integrable nonlinear equation has also been emphasized. The evolution of one and two-soliton solution with respect to time and space has been discussed in detail. The collision among the solitons has been manifested through an example of two-soliton case, revealing the elastic essence of the collision and the invariance of the soliton form and characteristics.展开更多
基金Supported by the National Natural Science Foundation of China (10775105)
文摘Based on the method of Hirota＇s bilinear derivative transform, the derivative nonlinear Schrodinger equation with vanishing boundary condition has been directly solved. The oneand two-soliton solutions are given as two typical examples in the illustration of the general procedures and the concrete cut-off technique of the series-form solution, and the n-soliton solution is also attained by induction method. Our study shows their equivalence to the existing soliton solutions by a simple parameter transformation. The methodological importance of bilinear derivative transform in dealing with an integrable nonlinear equation has also been emphasized. The evolution of one and two-soliton solution with respect to time and space has been discussed in detail. The collision among the solitons has been manifested through an example of two-soliton case, revealing the elastic essence of the collision and the invariance of the soliton form and characteristics.
