This paper proposes a method for constructing partial differential equation (PDE) systems with chaotic solitons by using truncated normal forms of an ordinary differential equation (ODE). The construction is based mainly on the fact that the existence of a soliton in a PDE system is equal to that of a homoclinic orbit in a related ODE system, and that chaos of ?i’lnikov homoclinic type in the ODE imply that the soliton in the PDE changes its profile chaotically along propagation direction. It is guaranteed that the constructed systems can self-generate chaotic solitons without any external perturbation but with constrained wave velocities in a rigorously mathematical sense.
展开▼
机译:两岸四地累犯制度比较研究——兼论中国内地累犯制度一体化之构想 =Comparative Study on Recidivism System in Hong Kong, Macao, Taiwan and China: Concurrently Discuss the Conception of Recidivism System Integration in Mainland China