In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family of isometric immersions from M^(n1) (c_1)×M^(n2)(c_2) to space forms M^n(c) by introducin...In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family of isometric immersions from M^(n1) (c_1)×M^(n2)(c_2) to space forms M^n(c) by introducing 2-parameter loop algebra.展开更多
Nonlocal physics is applied for investigation of the tsunami wave movement. It is established that tsunami movement and the Hubble effect of the Universe expansion can be considered in the frame of the same mathematic...Nonlocal physics is applied for investigation of the tsunami wave movement. It is established that tsunami movement and the Hubble effect of the Universe expansion can be considered in the frame of the same mathematical theory. Moreover, it can be said that tsunami is Hubble effect in the Earth conditions. The corresponding results of mathematical modeling are shown.展开更多
A （2 ＋ 1）-dimensional generalized Bogoyavlensky-Konopelchenko equation that possesses a Hirota bilinear form is considered. Starting with its Hirota bilinear form, a class of explicit lump solutions is computed thr...A （2 ＋ 1）-dimensional generalized Bogoyavlensky-Konopelchenko equation that possesses a Hirota bilinear form is considered. Starting with its Hirota bilinear form, a class of explicit lump solutions is computed through conducting symbolic computations with Maple, and a few plots of a specific presented lump solution are made to shed light on the characteristics of lumps. The result provides a new example of （2 ＋ 1）-dimensional nonlinear partial differential equations which possess lump solutions.展开更多
Multi-place nonlocal systems have attracted attention from many scientists.In this paper,we mainly review the recent progresses on two-place nonlocal systems(Alice-Bob systems)and four-place nonlocal models.Multi-plac...Multi-place nonlocal systems have attracted attention from many scientists.In this paper,we mainly review the recent progresses on two-place nonlocal systems(Alice-Bob systems)and four-place nonlocal models.Multi-place systems can firstly be derived from many physical problems by using a multiple scaling method with a discrete symmetry group including parity,time reversal,charge conjugates,rotations,field reversal and exchange transformations.Multiplace nonlocal systems can also be derived from the symmetry reductions of coupled nonlinear systems via discrete symmetry reductions.On the other hand,to solve multi-place nonlocal systems,one can use the symmetry-antisymmetry separation approach related to a suitable discrete symmetry group,such that the separated systems are coupled local ones.By using the separation method,all the known powerful methods used in local systems can be applied to nonlocal cases.In this review article,we take two-place and four-place nonlocal nonlinear Schr?dinger(NLS)systems and Kadomtsev-Petviashvili(KP)equations as simple examples to explain how to derive and solve them.Some types of novel physical and mathematical points related to the nonlocal systems are especially emphasized.展开更多
基金This work is partially surpported by NNSFC under No. 198111001by the Armored Force Engineering Institute
文摘In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family of isometric immersions from M^(n1) (c_1)×M^(n2)(c_2) to space forms M^n(c) by introducing 2-parameter loop algebra.
文摘Nonlocal physics is applied for investigation of the tsunami wave movement. It is established that tsunami movement and the Hubble effect of the Universe expansion can be considered in the frame of the same mathematical theory. Moreover, it can be said that tsunami is Hubble effect in the Earth conditions. The corresponding results of mathematical modeling are shown.
基金Acknowledgements The work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11301454, 11301331, 11371086, 11571079, 51771083）, the NSF under the grant DMS-1664561, the Jiangsu Qing Lan Project for Excellent Young Teachers in University （2014）, the Six Talent Peaks Project in Jiangsu Province （2016-JY-081）, the Natural Science Foundation for Colleges and Universities in Jiangsu Province （17KJB110020）, the Natural Science Foundation of Jiangsu Province （Grant No. BK20151160）, the Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT under Grant No. 2017XKZDll, and the Distinguished Professorships by Shanghai University of Electric Power and Shanghai Polytechnic University.
文摘A （2 ＋ 1）-dimensional generalized Bogoyavlensky-Konopelchenko equation that possesses a Hirota bilinear form is considered. Starting with its Hirota bilinear form, a class of explicit lump solutions is computed through conducting symbolic computations with Maple, and a few plots of a specific presented lump solution are made to shed light on the characteristics of lumps. The result provides a new example of （2 ＋ 1）-dimensional nonlinear partial differential equations which possess lump solutions.
基金sponsored by the National Natural Science Foundations of China(No.11975131,11435005)K C Wong Magna Fund in Ningbo University。
文摘Multi-place nonlocal systems have attracted attention from many scientists.In this paper,we mainly review the recent progresses on two-place nonlocal systems(Alice-Bob systems)and four-place nonlocal models.Multi-place systems can firstly be derived from many physical problems by using a multiple scaling method with a discrete symmetry group including parity,time reversal,charge conjugates,rotations,field reversal and exchange transformations.Multiplace nonlocal systems can also be derived from the symmetry reductions of coupled nonlinear systems via discrete symmetry reductions.On the other hand,to solve multi-place nonlocal systems,one can use the symmetry-antisymmetry separation approach related to a suitable discrete symmetry group,such that the separated systems are coupled local ones.By using the separation method,all the known powerful methods used in local systems can be applied to nonlocal cases.In this review article,we take two-place and four-place nonlocal nonlinear Schr?dinger(NLS)systems and Kadomtsev-Petviashvili(KP)equations as simple examples to explain how to derive and solve them.Some types of novel physical and mathematical points related to the nonlocal systems are especially emphasized.
