The widespread popularization and application of laser technology have provided a powerful tool for a deeper understanding of the material world and given birth to several emerging research fields.This study mainly fo...The widespread popularization and application of laser technology have provided a powerful tool for a deeper understanding of the material world and given birth to several emerging research fields.This study mainly focuses on the following three key aspects.First,the classical ensemble method is adopted to conduct a comprehensive and in-depth analysis of two-dimensional(2D)matter–wave pulses in Bose–Fermi mixed gases(including linear and nonlinear pulses).Second,under the strict constraints of unitary systems,a coupled Kd V equation is successfully derived,and the prolongation structure theory is skillfully used to carry out detailed calculations and analyses on this equation.Thus,the prolongation algebra of this equation is accurately determined,and the corresponding Lax pair is rigorously derived.Finally,based on the carefully obtained Lax pair from the prolongation structure theory,the soliton solutions of this equation are further analyzed in depth,and intuitive images of each soliton solution are carefully drawn.This lays a solid foundation for subsequent detailed research on these soliton characteristics and provides great convenience.展开更多
This study presents a(2+1)-dimensional complex coupled dispersionless system.A Lax pair is proposed,and the Darboux transformation is employed to construct multisoliton solutions.These solutions exhibit a range of wav...This study presents a(2+1)-dimensional complex coupled dispersionless system.A Lax pair is proposed,and the Darboux transformation is employed to construct multisoliton solutions.These solutions exhibit a range of wave phenomena,including bright and dark solitons,S-shaped formations,parabolic profiles,and periodic wave patterns.Additionally,it is shown that the system is equivalent to the sine-Gordon equation and the negative flow of the modified Korteweg-de Vries hierarchy through appropriate transformations.展开更多
The aim of this paper is to study an extended modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff(mKdV-CBS)equation and present its Lax pair with a spectral parameter.Meanwhile,a Miura transformation is explored...The aim of this paper is to study an extended modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff(mKdV-CBS)equation and present its Lax pair with a spectral parameter.Meanwhile,a Miura transformation is explored,which reveals the relationship between solutions of the extended mKdV-CBS equation and the extended(2+1)-dimensional Korteweg-de Vries(KdV)equation.On the basis of the obtained Lax pair and the existing research results,the Darboux transformation is derived,which plays a crucial role in presenting soliton solutions.In addition,soliton molecules are given by the velocity resonance mechanism.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.12261072)。
文摘The widespread popularization and application of laser technology have provided a powerful tool for a deeper understanding of the material world and given birth to several emerging research fields.This study mainly focuses on the following three key aspects.First,the classical ensemble method is adopted to conduct a comprehensive and in-depth analysis of two-dimensional(2D)matter–wave pulses in Bose–Fermi mixed gases(including linear and nonlinear pulses).Second,under the strict constraints of unitary systems,a coupled Kd V equation is successfully derived,and the prolongation structure theory is skillfully used to carry out detailed calculations and analyses on this equation.Thus,the prolongation algebra of this equation is accurately determined,and the corresponding Lax pair is rigorously derived.Finally,based on the carefully obtained Lax pair from the prolongation structure theory,the soliton solutions of this equation are further analyzed in depth,and intuitive images of each soliton solution are carefully drawn.This lays a solid foundation for subsequent detailed research on these soliton characteristics and provides great convenience.
文摘This study presents a(2+1)-dimensional complex coupled dispersionless system.A Lax pair is proposed,and the Darboux transformation is employed to construct multisoliton solutions.These solutions exhibit a range of wave phenomena,including bright and dark solitons,S-shaped formations,parabolic profiles,and periodic wave patterns.Additionally,it is shown that the system is equivalent to the sine-Gordon equation and the negative flow of the modified Korteweg-de Vries hierarchy through appropriate transformations.
基金supported by the National Natural Science Foundation of China(Grant No.12271488)。
文摘The aim of this paper is to study an extended modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff(mKdV-CBS)equation and present its Lax pair with a spectral parameter.Meanwhile,a Miura transformation is explored,which reveals the relationship between solutions of the extended mKdV-CBS equation and the extended(2+1)-dimensional Korteweg-de Vries(KdV)equation.On the basis of the obtained Lax pair and the existing research results,the Darboux transformation is derived,which plays a crucial role in presenting soliton solutions.In addition,soliton molecules are given by the velocity resonance mechanism.
