A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrodinger equation with wave operator

作者：Brugnano, Luigi; Zhang, Chengjian^*; Li, Dongfang

来源：Communications in Nonlinear Science & Numerical Simulation, 2018, 60: 33-49.

DOI：10.1016/j.cnsns.2017.12.018

• Nonlinear Schrodinger equation
• Hamiltonian problem
• Wave operator
• Energy-conserving methods
• Hamiltonian boundary value methods

In this paper, we study the efficient solution of the nonlinear Schrodinger equation with wave operator, subject to periodic boundary conditions. In such a case, it is known that its solution conserves a related functional. By using a Fourier expansion in space, the problem is at first casted into Hamiltonian form, with the same Hamiltonian functional. A Fourier-Galerkin space semi-discretization then provides a large-size Hamiltonian ODE problem, whose solution in time is carried out by means of energy-conserving methods in the HBVM class (Hamiltonian boundary value methods). The efficient implementation of the methods for the resulting problem is also considered and some numerical examples are reported.

• 出版日期2018-7
• 单位华中科技大学