Article citationsMore>>

V. I. Arnold, “Lectures in Bifurcation in Versal Families,” Russian Mathematical Surveys, Vol. 27, No. 5, 1972, pp. 54-123. doi:10.1070/RM1972v027n05ABEH001385

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.