The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type ...The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.展开更多
For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characteri...For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems.展开更多
文摘The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.
基金Supported by Nature Science Foundation of Hainan Province (Grant No. 118MS040,2018CXTD338)NSF of Higher Education Institutions of Hainan Province (Grant No. Hnky2018ZD-6)National Natural Science Foundation of China (Grant No. 11861029)。
文摘For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems.
