TY - JOUR
T1 - Almost structure-preserving analysis for weakly linear damping nonlinear Schrödinger equation with periodic perturbation
AU - Hu, Weipeng
AU - Deng, Zichen
AU - Yin, Tingting
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - Exploring the dynamic behaviors of the damping nonlinear Schrödinger equation (NLSE) with periodic perturbation is a challenge in the field of nonlinear science, because the numerical approaches available for damping-driven dynamic systems may exhibit the artificial dissipation in different degree. In this paper, based on the generalized multi-symplectic idea, the local energy/momentum loss expressions as well as the approximate symmetric form of the linearly damping NLSE with periodic perturbation are deduced firstly. And then, the local energy/momentum losses are separated from the simulation results of the NLSE with small linear damping rate less than the threshold to insure structure-preserving properties of the scheme. Finally, the breakup process of the multisoliton state is simulated and the bifurcation of the discrete eigenvalues of the associated Zakharov-Shabat spectral problem is obtained to investigate the variation of the velocity as well as the amplitude of the solitons during the splitting process.
AB - Exploring the dynamic behaviors of the damping nonlinear Schrödinger equation (NLSE) with periodic perturbation is a challenge in the field of nonlinear science, because the numerical approaches available for damping-driven dynamic systems may exhibit the artificial dissipation in different degree. In this paper, based on the generalized multi-symplectic idea, the local energy/momentum loss expressions as well as the approximate symmetric form of the linearly damping NLSE with periodic perturbation are deduced firstly. And then, the local energy/momentum losses are separated from the simulation results of the NLSE with small linear damping rate less than the threshold to insure structure-preserving properties of the scheme. Finally, the breakup process of the multisoliton state is simulated and the bifurcation of the discrete eigenvalues of the associated Zakharov-Shabat spectral problem is obtained to investigate the variation of the velocity as well as the amplitude of the solitons during the splitting process.
KW - Breakup of multisoliton state
KW - Damping nonlinear Schrödinger equation
KW - Generalized multi-symplectic
KW - Periodic perturbation
KW - Structure-preserving
UR - http://www.scopus.com/inward/record.url?scp=84973320504&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2016.05.024
DO - 10.1016/j.cnsns.2016.05.024
M3 - 文章
AN - SCOPUS:84973320504
SN - 1007-5704
VL - 42
SP - 298
EP - 312
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
ER -