In this paper,by using the Darboux transformation(DT)method and the Taylor expansion method,a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-D...In this paper,by using the Darboux transformation(DT)method and the Taylor expansion method,a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-DNLS equation is constructed when n is even.Breathers and rogue waves can be obtained from this determinant,respectively.Further to this,the hybrid rogue waves and breathers solutions on the different periodic backgrounds are given explicitly,including the single-periodic background,the double-periodic background and the plane wave background by selecting different parameters.In addition,the form of the obtained solutions is summarized.展开更多
By analyzing the basic rules and measurement principles of the sustainable utilization of ecological. resources and constructing its mathematical model this paper points out that the sustainable utilization of ecologi...By analyzing the basic rules and measurement principles of the sustainable utilization of ecological. resources and constructing its mathematical model this paper points out that the sustainable utilization of ecological resources is in nature to use the double-period model thousands of times for the dynamic distribution of ecological resources effectively. And it points out that in order to realize the sustainable utilization of ecological resources we must follow the basw principle-non-decreasing ecological capital and put forward corresponding standards, measures, policies and proposals.展开更多
We theoretically study the beam dynamical behaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal. We find that two different Bloch oscillation patterns appear for...We theoretically study the beam dynamical behaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal. We find that two different Bloch oscillation patterns appear for the excitation of both broad and narrow light beams. One kind of optical Landau-Zener tunnelling also appears upon the Bloch oscillation and can be controlled by adjusting the parameter of the optical lattice. Unlike the case of linear potential, the energy radiation due to Landau-Zener tunnelling can be confined in modulated lattices of this kind. For high input intensity levels, the Landau-Zener tunnelling is suppressed by the photovoltaic photorefractive nonlinearity and a symmetry breaking of beam propagation from the modulational instability appears.展开更多
基金supported by the National Natural Science Foundation of China under(Grant No.12361052)the Natural Science Foundation of Inner Mongolia Autonomous Region China under(Grant No.2020LH01010,2022ZD05)+1 种基金Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2414)the Fundamental Research Founds for the Inner Mongolia Normal University(Grant No.2022JBTD007).
文摘In this paper,by using the Darboux transformation(DT)method and the Taylor expansion method,a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-DNLS equation is constructed when n is even.Breathers and rogue waves can be obtained from this determinant,respectively.Further to this,the hybrid rogue waves and breathers solutions on the different periodic backgrounds are given explicitly,including the single-periodic background,the double-periodic background and the plane wave background by selecting different parameters.In addition,the form of the obtained solutions is summarized.
文摘By analyzing the basic rules and measurement principles of the sustainable utilization of ecological. resources and constructing its mathematical model this paper points out that the sustainable utilization of ecological resources is in nature to use the double-period model thousands of times for the dynamic distribution of ecological resources effectively. And it points out that in order to realize the sustainable utilization of ecological resources we must follow the basw principle-non-decreasing ecological capital and put forward corresponding standards, measures, policies and proposals.
基金Project supported by the National Natural Science Foundation of China (Grant No 10874251)
文摘We theoretically study the beam dynamical behaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal. We find that two different Bloch oscillation patterns appear for the excitation of both broad and narrow light beams. One kind of optical Landau-Zener tunnelling also appears upon the Bloch oscillation and can be controlled by adjusting the parameter of the optical lattice. Unlike the case of linear potential, the energy radiation due to Landau-Zener tunnelling can be confined in modulated lattices of this kind. For high input intensity levels, the Landau-Zener tunnelling is suppressed by the photovoltaic photorefractive nonlinearity and a symmetry breaking of beam propagation from the modulational instability appears.
