The(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model.By using the long wave limit method and confining the conjugation conditions on the interrelated solitons,the gener...The(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model.By using the long wave limit method and confining the conjugation conditions on the interrelated solitons,the general M-lump,high-order breather,and localized interaction hybrid solutions are investigated,respectively.Then we implement the numerical simulations to research their dynamical behaviors,which indicate that different parameters have very different dynamic properties and propagation modes of the waves.The method involved can be validly employed to get high-order waves and study their propagation phenomena of many nonlinear equations.展开更多
In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton ...In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.展开更多
Lump solutions are one of the most common solutions for nonlinear evolution equations.This study aspires to investigate the generalized Hietarintatype equation.We auspiciously provide multiple M-lump waves.On the othe...Lump solutions are one of the most common solutions for nonlinear evolution equations.This study aspires to investigate the generalized Hietarintatype equation.We auspiciously provide multiple M-lump waves.On the other hand,collision phenomena to multiple M-lump waves with soliton wave solutions are also provided.During the collision,the amplitude of the lump will change significantly over the processes,whereas the amplitude of the soliton will just minimally alter.As it is of paramount importance,we use suitable values of parameter to put out the physical features of the reported results through three dimensional and contour graphics.The results presented express physical features of lump and lump interaction phenomena of different kinds of nonlinear physical processes.Further,this study serves to enrich nonlinear dynamics and provide insight into how nonlinear waves propagate.展开更多
基金The work was supported by the National Natural Science Foundation of China(Grant Nos.11371086,11671258,11975145)the Fund of Science and Technology Commission of Shanghai Municipality(No.13ZR1400100)the Fund of Donghua University,Institute for Nonlinear Sciences,and the Fundamental Research Funds for the Central Universitieswith contract number 2232021G-13.
文摘The(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model.By using the long wave limit method and confining the conjugation conditions on the interrelated solitons,the general M-lump,high-order breather,and localized interaction hybrid solutions are investigated,respectively.Then we implement the numerical simulations to research their dynamical behaviors,which indicate that different parameters have very different dynamic properties and propagation modes of the waves.The method involved can be validly employed to get high-order waves and study their propagation phenomena of many nonlinear equations.
文摘In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.
文摘Lump solutions are one of the most common solutions for nonlinear evolution equations.This study aspires to investigate the generalized Hietarintatype equation.We auspiciously provide multiple M-lump waves.On the other hand,collision phenomena to multiple M-lump waves with soliton wave solutions are also provided.During the collision,the amplitude of the lump will change significantly over the processes,whereas the amplitude of the soliton will just minimally alter.As it is of paramount importance,we use suitable values of parameter to put out the physical features of the reported results through three dimensional and contour graphics.The results presented express physical features of lump and lump interaction phenomena of different kinds of nonlinear physical processes.Further,this study serves to enrich nonlinear dynamics and provide insight into how nonlinear waves propagate.
