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In this paper, the discrete gradient methods are investigated for ODEs with 痳st integral, and the recursive formula is presented for deriving the high-order numerical methods. We generalize the idea...
In this paper, we study the preservation of quadratic conservation laws of Runge-Kutta methods and partitioned Runge-Kutta methods for Hamiltonian PDEs and establish the relation between multi-sympl...
Abstract: We consider a ground state (soliton) of a Hamiltonian PDE. We prove that if the soliton is orbitally stable then it is also asymptotically stable. The main assumptions are transversal nondeg...
Abstract: We consider a Hamiltonian systems which is invariant under a one-parameter unitary group. We give a criterion for the stability and instability of bound states for the degenerate case. We ap...
In this article we consider partitioned Runge-Kutta (PRK) methods for Hamiltonian partial differential equations (PDEs), and present some sufficient conditions for multi-symplecticity of PRK methods o...

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