In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the repr...In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.展开更多
The significance of laser-driven polarized beam acceleration has been increasingly recognized in recent years.We propose an efficient method for generating polarized proton beams from a pre-polarized hydrogen halide g...The significance of laser-driven polarized beam acceleration has been increasingly recognized in recent years.We propose an efficient method for generating polarized proton beams from a pre-polarized hydrogen halide gas jet,utilizing magnetic vortex acceleration enhanced by a laser-driven plasma bubble.When a petawatt laser pulse passes through a pre-polarized gas jet,a bubble-like ultra-nonlinear plasma wave is formed.As a portion of the particles constituting this wave,background protons are swept by the acceleration field of the bubble and oscillate significantly along the laser propagation axis.Some of the pre-accelerated protons in the plasma wave are trapped by the acceleration field at the rear side of the target.This acceleration field is intensified by the transverse expansion of the laser-driven magnetic vortex,resulting in energetic polarized proton beams.The spin of energetic protons is determined by their precession within the electromagnetic field,which is described using the Thomas-Bargmann-Michel-Telegdi equation in analytical models and particle-in-cell simulations.Multidimensional simulations reveal that monoenergetic proton beams with an energy of hundreds of MeV,a beam charge of hundreds of pC,and a beam polarization of tens of percent can be produced at laser powers of several petawatts.Such laser-driven polarized proton beams have promise for application in polarized beam colliders,where they can be utilized to investigate particle interactions and to explore the properties of matter under extreme conditions.展开更多
In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax ...In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax pair under the Bargmann constraint. It is also shown that the potential u in the stationary Sehrodinger equation can be a summation of squares of wave functions from bilinear point of view.展开更多
Based on the conclusion that the generalized Bargmann representation of a two-mode Fock state is a two-variable Hermite polynomial function /Hong-Yi Fan and Jun-hua Chen,Phys.Lett.A303(2002)311] we derive the generali...Based on the conclusion that the generalized Bargmann representation of a two-mode Fock state is a two-variable Hermite polynomial function /Hong-Yi Fan and Jun-hua Chen,Phys.Lett.A303(2002)311] we derive the generalized Bargmann representation of the spin coherent state and some new relations in the generalized function space.展开更多
In this paper a finite dimensional Liouville completely integrable system With timedependent coefficients: H=1/2(P,P) +1/2 t-3 (q,Aq) -1/8 t-9/2 (q,q)2, is obtained. It is proved that when (p,q) satisfies two noninvo...In this paper a finite dimensional Liouville completely integrable system With timedependent coefficients: H=1/2(P,P) +1/2 t-3 (q,Aq) -1/8 t-9/2 (q,q)2, is obtained. It is proved that when (p,q) satisfies two noninvolutive systems (H) and (F1), the constraint u =1 /2t-9/2 (q,q) - 7x/(12t) gives a solution of generalized CKdV equation.展开更多
By means of Hirota method,N-soliton solutions of the modified KdV equation under the Bargmannconstraint are obtained through solving the Bargmann constraint and the related Lax pair and conjugate Lax pair ofthe modifi...By means of Hirota method,N-soliton solutions of the modified KdV equation under the Bargmannconstraint are obtained through solving the Bargmann constraint and the related Lax pair and conjugate Lax pair ofthe modified KdV equation.展开更多
In this paper, a new spectral problem is proposed and the corresponding soliton equations hierarchy are also obtained. Under a constraint between the potentials and the eigenfunctions, the eigenvalue problem is nonlin...In this paper, a new spectral problem is proposed and the corresponding soliton equations hierarchy are also obtained. Under a constraint between the potentials and the eigenfunctions, the eigenvalue problem is nonlinearized so as to be a new finite-dimensional Hamiltonian system. By resotring to the generating function approach, we obtain conserved integrals and the involutivity of the conserved integrals. The finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense. Finally, we show the decomposition of the soliton equations.展开更多
文摘In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.
基金supported by the National Natural Science Foundation of China(Grant Nos.12075081 and 12404395)the Innovation Group Project of the Natural Science Foundation of Hubei Province of China(Grant No.2024AFA038)Bin Liu acknowledges the support of Guangdong High Level Innovation Research Institute Project,Grant No.2021B0909050006.
文摘The significance of laser-driven polarized beam acceleration has been increasingly recognized in recent years.We propose an efficient method for generating polarized proton beams from a pre-polarized hydrogen halide gas jet,utilizing magnetic vortex acceleration enhanced by a laser-driven plasma bubble.When a petawatt laser pulse passes through a pre-polarized gas jet,a bubble-like ultra-nonlinear plasma wave is formed.As a portion of the particles constituting this wave,background protons are swept by the acceleration field of the bubble and oscillate significantly along the laser propagation axis.Some of the pre-accelerated protons in the plasma wave are trapped by the acceleration field at the rear side of the target.This acceleration field is intensified by the transverse expansion of the laser-driven magnetic vortex,resulting in energetic polarized proton beams.The spin of energetic protons is determined by their precession within the electromagnetic field,which is described using the Thomas-Bargmann-Michel-Telegdi equation in analytical models and particle-in-cell simulations.Multidimensional simulations reveal that monoenergetic proton beams with an energy of hundreds of MeV,a beam charge of hundreds of pC,and a beam polarization of tens of percent can be produced at laser powers of several petawatts.Such laser-driven polarized proton beams have promise for application in polarized beam colliders,where they can be utilized to investigate particle interactions and to explore the properties of matter under extreme conditions.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10871165 and 10671121
文摘In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax pair under the Bargmann constraint. It is also shown that the potential u in the stationary Sehrodinger equation can be a summation of squares of wave functions from bilinear point of view.
文摘Based on the conclusion that the generalized Bargmann representation of a two-mode Fock state is a two-variable Hermite polynomial function /Hong-Yi Fan and Jun-hua Chen,Phys.Lett.A303(2002)311] we derive the generalized Bargmann representation of the spin coherent state and some new relations in the generalized function space.
文摘In this paper a finite dimensional Liouville completely integrable system With timedependent coefficients: H=1/2(P,P) +1/2 t-3 (q,Aq) -1/8 t-9/2 (q,q)2, is obtained. It is proved that when (p,q) satisfies two noninvolutive systems (H) and (F1), the constraint u =1 /2t-9/2 (q,q) - 7x/(12t) gives a solution of generalized CKdV equation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10371070 and 10671121
文摘By means of Hirota method,N-soliton solutions of the modified KdV equation under the Bargmannconstraint are obtained through solving the Bargmann constraint and the related Lax pair and conjugate Lax pair ofthe modified KdV equation.
基金Supported by the National Natural Science Foundation of China(1127100861072147+2 种基金11447220)Supported by the First-class Discipline of Universities in ShanghaiSupported by the Science and Technology Department of Henan Province(152300410230)
文摘In this paper, a new spectral problem is proposed and the corresponding soliton equations hierarchy are also obtained. Under a constraint between the potentials and the eigenfunctions, the eigenvalue problem is nonlinearized so as to be a new finite-dimensional Hamiltonian system. By resotring to the generating function approach, we obtain conserved integrals and the involutivity of the conserved integrals. The finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense. Finally, we show the decomposition of the soliton equations.
