The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is stu...The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is studied in this paper. When the physical parameters transpass the boundaries, the solutions of period T =2π/ω will lose their stability, and the solutions of period T =2π/ω take place. Continuous period doubling bifurcations lead to chaos.展开更多
The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysi...The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.展开更多
The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity...The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.展开更多
文摘The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is studied in this paper. When the physical parameters transpass the boundaries, the solutions of period T =2π/ω will lose their stability, and the solutions of period T =2π/ω take place. Continuous period doubling bifurcations lead to chaos.
基金supported by the"Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues"of the Chinese Academy of Sciences (Grant No.XDA01020304)
文摘The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.
基金supported by the National Natural Science Foundation of China(No.11201292)Shanghai Natural Science Foundation(No.12ZR1444300)the Key Discipline"Applied Mathematics"of Shanghai Second Polytechnic University(No.XXKZD1304)
文摘The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.
