We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations.Based on the Hirota bilinear method and the test function method,we construct the exact solutions to th...We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations.Based on the Hirota bilinear method and the test function method,we construct the exact solutions to the extended equations including lump solutions,lump–kink solutions,and two other types of interaction solutions,by solving the underdetermined nonlinear system of algebraic equations for associated parameters.Finally,analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed.展开更多
Since 2013,China has been the world’s largest market for industrial robots.Despite the gradual maturity of the industrial robot system,the lagging R&D and backward technology level of industrial robots have led t...Since 2013,China has been the world’s largest market for industrial robots.Despite the gradual maturity of the industrial robot system,the lagging R&D and backward technology level of industrial robots have led to a strong dependence on the import of core components and key technologies,which to a certain extent has restricted the development and improvement of industrial robots.At present,the“neck problem”in the field of industrial robots in China is not only in the reducer,controller,and servo but also in the basic processing equipment,basic technology,and basic materials.In this paper,we propose measures to improve the“neck problem”of industrial robots to promote the high-quality development of industrial robots in China.展开更多
Based on the long wave limit method,the general form of the second-order and third-order rogue wave solutions to the focusing nonlinear Schr?dinger equation are given by introducing some arbitrary parameters.The inter...Based on the long wave limit method,the general form of the second-order and third-order rogue wave solutions to the focusing nonlinear Schr?dinger equation are given by introducing some arbitrary parameters.The interaction solutions between the first-order rogue wave and one-breather wave are constructed by taking a long wave limit on the two-breather solutions.By applying the same method to the three-breather solutions,two types of interaction solutions are obtained,namely the first-order rogue wave and two breather waves,the second-order rogue wave and one-breather wave,respectively.The influence of the parameters related to the phase on the interaction phenomena is graphically demonstrated.Collisions occur among the rogue waves and breather waves.After the collisions,the shape of them remains unchanged.The abundant interaction phenomena in this paper will contribute to a better understanding of the propagation and control of nonlinear waves.展开更多
In this paper,we propose a combined form of the bilinear Kadomtsev-Petviashvili equation and the bilinear extended(2+1)-dimensional shallow water wave equation,which is linked with a novel(2+1)-dimensional nonlinear m...In this paper,we propose a combined form of the bilinear Kadomtsev-Petviashvili equation and the bilinear extended(2+1)-dimensional shallow water wave equation,which is linked with a novel(2+1)-dimensional nonlinear model.This model might be applied to describe the evolution of nonlinear waves in the ocean.Under the effect of a novel combination of nonlinearity and dispersion terms,two cases of lump solutions to the(2+1)-dimensional nonlinear model are derived by searching for the quadratic function solutions to the bilinear form.Moreover,the one-lump-multi-stripe solutions are constructed by the test function combining quadratic functions and multiple exponential functions.The one-lump-multi-soliton solutions are derived by the test function combining quadratic functions and multiple hyperbolic cosine functions.Dynamic behaviors of the lump solutions and mixed solutions are analyzed via numerical simulation.The result is of importance to provide efficient expressions to model nonlinear waves and explain some interaction mechanism of nonlinear waves in physics.展开更多
基金Project supported by the Fundamental Research Funds for the Central Universities of China(Grant No.2018RC031)the National Natural Science Foundation of China(Grant No.71971015)+1 种基金the Program of the Co-Construction with Beijing Municipal Commission of Education of China(Grant Nos.B19H100010and B18H100040)the Open Fund of IPOC(BUPT)。
文摘We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations.Based on the Hirota bilinear method and the test function method,we construct the exact solutions to the extended equations including lump solutions,lump–kink solutions,and two other types of interaction solutions,by solving the underdetermined nonlinear system of algebraic equations for associated parameters.Finally,analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed.
文摘Since 2013,China has been the world’s largest market for industrial robots.Despite the gradual maturity of the industrial robot system,the lagging R&D and backward technology level of industrial robots have led to a strong dependence on the import of core components and key technologies,which to a certain extent has restricted the development and improvement of industrial robots.At present,the“neck problem”in the field of industrial robots in China is not only in the reducer,controller,and servo but also in the basic processing equipment,basic technology,and basic materials.In this paper,we propose measures to improve the“neck problem”of industrial robots to promote the high-quality development of industrial robots in China.
基金supported by the National Natural Science Foundation of China under Grant No.12275017the Beijing Laboratory of National Economic Security Early-warning Engineering,Beijing Jiaotong University。
文摘Based on the long wave limit method,the general form of the second-order and third-order rogue wave solutions to the focusing nonlinear Schr?dinger equation are given by introducing some arbitrary parameters.The interaction solutions between the first-order rogue wave and one-breather wave are constructed by taking a long wave limit on the two-breather solutions.By applying the same method to the three-breather solutions,two types of interaction solutions are obtained,namely the first-order rogue wave and two breather waves,the second-order rogue wave and one-breather wave,respectively.The influence of the parameters related to the phase on the interaction phenomena is graphically demonstrated.Collisions occur among the rogue waves and breather waves.After the collisions,the shape of them remains unchanged.The abundant interaction phenomena in this paper will contribute to a better understanding of the propagation and control of nonlinear waves.
基金supported by the Project of the Fundamental Research Funds for the Central Universities of China(2022JBMC034)the National Natural Science Foundation of China under Grant No.12275017Beijing Laboratory of National Economic Security Early-warning Engineering,Beijing Jiaotong University
文摘In this paper,we propose a combined form of the bilinear Kadomtsev-Petviashvili equation and the bilinear extended(2+1)-dimensional shallow water wave equation,which is linked with a novel(2+1)-dimensional nonlinear model.This model might be applied to describe the evolution of nonlinear waves in the ocean.Under the effect of a novel combination of nonlinearity and dispersion terms,two cases of lump solutions to the(2+1)-dimensional nonlinear model are derived by searching for the quadratic function solutions to the bilinear form.Moreover,the one-lump-multi-stripe solutions are constructed by the test function combining quadratic functions and multiple exponential functions.The one-lump-multi-soliton solutions are derived by the test function combining quadratic functions and multiple hyperbolic cosine functions.Dynamic behaviors of the lump solutions and mixed solutions are analyzed via numerical simulation.The result is of importance to provide efficient expressions to model nonlinear waves and explain some interaction mechanism of nonlinear waves in physics.