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

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DOI: 10.4236/am.2012.37112    5,244 Downloads   7,502 Views   Citations
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ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

B. Chen, "An Approach for the Construction of Systems That Self-Generate Chaotic Solitons," Applied Mathematics, Vol. 3 No. 7, 2012, pp. 755-759. doi: 10.4236/am.2012.37112.

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