This paper presents a geometric perspective that connects reciprocal transformations with multidimensional integrable deformations.By interpreting conservation laws as closed 1-forms,we formalize reciprocal transforma...This paper presents a geometric perspective that connects reciprocal transformations with multidimensional integrable deformations.By interpreting conservation laws as closed 1-forms,we formalize reciprocal transformations as induced local diffeomorphisms on the jet bundle.This allows us to characterize higher-dimensional deformations as systematic fiber bundle extensions,where fiber coordinates are generated by potential functions of the conservation laws.This perspective provides an interpretation for the covariant lifting of Lax pairs to higher dimensions and reveals that auto-Backlund transformations are composite diffeomorphisms.These results are applied to several classical integrable models.展开更多
Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact sol...Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians.Realness of independent variables involved in the reciprocal transformations is verified.Dynamics of some obtained solutions are illustrated.展开更多
The Qiao-Liu equation with self-consistent sources (QLESCS) and its Lax representation are derived. A reciprocal transformation for the QLESCS is given. By making use of the reciprocal transformation and the solutions...The Qiao-Liu equation with self-consistent sources (QLESCS) and its Lax representation are derived. A reciprocal transformation for the QLESCS is given. By making use of the reciprocal transformation and the solutions of the mKdV equation with self-consistent sources (mKdVSCS), the solutions of the QLESCS are presented.展开更多
The link of(2+1)-dimensional Harry Dym equation with the modified Kadomtsev-Petviashvili equation by the reciprocal transformation is shown.With the help of Darboux transformation,exact solutions of the(2+1)-dimension...The link of(2+1)-dimensional Harry Dym equation with the modified Kadomtsev-Petviashvili equation by the reciprocal transformation is shown.With the help of Darboux transformation,exact solutions of the(2+1)-dimensional Harry Dym equation are constructed and represented in terms of Wronskians.展开更多
We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on...We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed.展开更多
基金sponsored by the National Natural Science Foundation of China(Nos.12235007,11975131)。
文摘This paper presents a geometric perspective that connects reciprocal transformations with multidimensional integrable deformations.By interpreting conservation laws as closed 1-forms,we formalize reciprocal transformations as induced local diffeomorphisms on the jet bundle.This allows us to characterize higher-dimensional deformations as systematic fiber bundle extensions,where fiber coordinates are generated by potential functions of the conservation laws.This perspective provides an interpretation for the covariant lifting of Lax pairs to higher dimensions and reveals that auto-Backlund transformations are composite diffeomorphisms.These results are applied to several classical integrable models.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11875040 and 12171308)
文摘Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians.Realness of independent variables involved in the reciprocal transformations is verified.Dynamics of some obtained solutions are illustrated.
基金Supported by National Basic Research Program of China (973 Program) under Grant No. 2007CB814800National Natural Science Foundation of China under Grant Nos. 10901090,11171175+1 种基金China Postdoctoral Science Foundation Funded Project under GrantNo. 20110490408Chinese Universities Scientific Fund under Grant No. 2011JS041
文摘The Qiao-Liu equation with self-consistent sources (QLESCS) and its Lax representation are derived. A reciprocal transformation for the QLESCS is given. By making use of the reciprocal transformation and the solutions of the mKdV equation with self-consistent sources (mKdVSCS), the solutions of the QLESCS are presented.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871471,11931017and 12171474)。
文摘The link of(2+1)-dimensional Harry Dym equation with the modified Kadomtsev-Petviashvili equation by the reciprocal transformation is shown.With the help of Darboux transformation,exact solutions of the(2+1)-dimensional Harry Dym equation are constructed and represented in terms of Wronskians.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11374270 and 11674294
文摘We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed.
