Deformation and (3+1)-dimensional integrable model

Science in China Series A Mathematics (Impact Factor: 0.7). 04/2012; 43(6):655-660. DOI: 10.1007/BF02908778


A suitable and effective deformation relation is derived by using the Miura transformation. In the light of this relation,
the (2 + 1)-dimensional linear heat conductive equation is deformed to a (3 + 1)-dimensional model. It is proved by standard
singularity structure analysis that the (3+1)-dimensional nonlinear equation obtained here is Painlevé integrable.

1 Follower
13 Reads
  • [Show abstract] [Hide abstract]
    ABSTRACT: The dynamical behavior of the perturbed compound KdV–Burgers equation is investigated numerically. It is shown that the chaotic dynamics can occur when the compound KdV–Burgers equation is perturbed by periodic forcing. Different routes to chaos such as period doubling, quasi-periodic routes, and the shapes of strange attractors are observed by applying bifurcation diagrams, the largest Lyapunov exponent, phase projection and Poincaré map.
    Chaos Solitons & Fractals 08/2007; 33(4-33):1307-1313. DOI:10.1016/j.chaos.2006.01.107 · 1.45 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: As a governing equation of wave propagation in a nonlinear, dispersive and dissipative media, KdV-Burgers type equation has received great attention. In this paper, the dynamical behavior of the generalized KdV-Burgers equation under a periodic perturbation is investigated numerically in detail. It is shown that dynamical chaos can occur when we choose appropriately systematic parameters and initial conditions. Abundant bifurcation structures and different routes to chaos such as period-doubling and inverse period-doubling cascades, intermittent bifurcation and crisis, are found by applying bifurcation diagrams, the Poincaré maps and phase portraits. To characterize chaotic behavior of this system, the spectrum of Lyapunov exponent and Lyapunov dimension of the attractor are also employed.
    International Journal of Bifurcation and Chaos 08/2012; 22(8). DOI:10.1142/S0218127412501933 · 1.08 Impact Factor