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
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.
