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
In this paper, we first obtain a bilinear form with small perturbation u_0 for a generalized(3+1)-dimensional nonlinear wave equation in liquid with gas bubbles. Based on that, a new bilinear B?cklund transformation w...In this paper, we first obtain a bilinear form with small perturbation u_0 for a generalized(3+1)-dimensional nonlinear wave equation in liquid with gas bubbles. Based on that, a new bilinear B?cklund transformation which consists of four bilinear equations and involves seven arbitrary parameters is constructed. After that, by applying a new symbolic computation method, we construct the higher order rogue waves with controllable center to the generalized(3+1)-dimensional nonlinear wave equation. The rogue waves present new structure, which contain two free parametersα and β. The dynamic properties of the higher order rogue waves are demonstrated graphically. The graphs tell that the parameters α and β can control the center of the rogue waves.展开更多
A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper＇s formants in different frequency ba...A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper＇s formants in different frequency bands, the spectrum of the whispered speech will be processed in the separate partitions of this paper. On the basis of this spectrum, we will establish a conversion function able to usefully convert whispered speech to normal speech. Because of the whisper＇s non-linear offset in relation to normal speech, this paper introduces an expansion factor in the bilinear transform function making it correspond more closely to the actual conversion demands of whispered speech to normal speech. The introduction of this factor takes the non-linear move of the spectrum and the compression of the formant bandwidth into consideration, thus effectively reducing the spectrum distortion distance in the conversion. The experiment results show that the conversion presented in this paper effectively improves both the sound quality and the intelligibility of whispered speech.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.
基金Supported by the National Natural Science Foundation of China(11471004,11501498)Shaanxi Key Research and Development Programs(2018SF-251)the Research Project at Yuncheng University [XK2012007]
文摘In this paper, we first obtain a bilinear form with small perturbation u_0 for a generalized(3+1)-dimensional nonlinear wave equation in liquid with gas bubbles. Based on that, a new bilinear B?cklund transformation which consists of four bilinear equations and involves seven arbitrary parameters is constructed. After that, by applying a new symbolic computation method, we construct the higher order rogue waves with controllable center to the generalized(3+1)-dimensional nonlinear wave equation. The rogue waves present new structure, which contain two free parametersα and β. The dynamic properties of the higher order rogue waves are demonstrated graphically. The graphs tell that the parameters α and β can control the center of the rogue waves.
基金supported by the National Natural Science Foundation of China(61271359,61071215)Suzhou Science and Technology Development Plan(SYG201001)Key Joint Laboratory of Soochow University and JieMei Biomedical Engineering Instrument
文摘A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper＇s formants in different frequency bands, the spectrum of the whispered speech will be processed in the separate partitions of this paper. On the basis of this spectrum, we will establish a conversion function able to usefully convert whispered speech to normal speech. Because of the whisper＇s non-linear offset in relation to normal speech, this paper introduces an expansion factor in the bilinear transform function making it correspond more closely to the actual conversion demands of whispered speech to normal speech. The introduction of this factor takes the non-linear move of the spectrum and the compression of the formant bandwidth into consideration, thus effectively reducing the spectrum distortion distance in the conversion. The experiment results show that the conversion presented in this paper effectively improves both the sound quality and the intelligibility of whispered speech.
