An Approach for the Construction of Systems That Self-Generate Chaotic Solitons

• 作者: Baoying Chen
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: CHAOTIC SOLITONS PARTIAL Differential Equation HOMOCLINIC ORBIT
• 年，卷（期）: 2012,（7）
• 页码范围: 755-759
• 页数: 5页
• 分类号: O1

摘要

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.