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P. H. Coullet and E. A. Spiegel, “Amplitude Equations for Systems with Competing Instabilities,” SIAM Journal on Applied Mathematics, Vol. 43, No. 4, 1983, pp. 776-821. doi:10.1137/0143052

has been cited by the following article:

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

    AUTHORS: Baoying Chen

    KEYWORDS: Chaotic Solitons; Partial Differential Equation; Homoclinic Orbit

    JOURNAL NAME: Applied Mathematics, Vol.3 No.7, June 19, 2012

    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.