Moving discrete breathers in a Klein–Gordon chain with an impurity

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein?Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity.

[1]  Moving breathers in a bent DNA model , 2002, nlin/0202007.

[2]  R. MacKay,et al.  Discrete breathers and Anderson modes: two faces of the same phenomenon? , 1999 .

[3]  Robert S. MacKay,et al.  Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators , 1994 .

[4]  B. Malomed.  Inelastic interactions of solitons in nearly integrable systems. I , 1985 .

[5]  F. Palmero,et al.  LETTER TO THE EDITOR: Numerical study of two-dimensional disordered Klein-Gordon lattices with cubic soft anharmonicity , 2001 .

[6]  Peyrard,et al.  Effective breather trapping mechanism for DNA transcription. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Sergej Flach.  Tangent bifurcation of band edge plane waves, dynamical symmetry breaking and vibrational localization , 1996 .

[8]  J. Archilla,et al.  Moving breathers in a DNA model with competing short- and long-range dispersive interactions , 2002 .

[9]  S. Aubry,et al.  Breathers in nonlinear lattices: existence, linear stability and quantization , 1997 .

[10]  Peyrard,et al.  Interaction of discrete breathers with impurity modes. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  J. M. Sancho,et al.  Dynamical properties of discrete breathers in curved chains with first and second neighbor interactions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Chen,et al.  Breather Mobility in Discrete phi4 Nonlinear Lattices. , 1996, Physical review letters.

[13]  F. Angulo-Brown,et al.  Symbolic dynamics of the cubic map , 1985 .

[14]  Serge Aubry,et al.  Breathers in nonlinear lattices: numerical calculation from the anticontinuous limit , 1996 .

[15]  Yuri S. Kivshar,et al.  Nonlinear dynamics of the Frenkel—Kontorova model , 1998 .

[16]  Y. Kivshar,et al.  DNA PROMOTERS AND NONLINEAR DYNAMICS , 1994 .

[17]  Y. Kivshar,et al.  Resonant kink-impurity interactions in the sine-Gordon model. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[18]  C. R. Willis,et al.  Discrete Breathers , 1997 .

[19]  Bishop,et al.  Statistical mechanics of a nonlinear model for DNA denaturation. , 1989, Physical review letters.

[20]  Li,et al.  Lattice-soliton scattering in nonlinear atomic chains. , 1988, Physical review. B, Condensed matter.

[21]  Kivshar,et al.  Nonlinear dynamics of the Frenkel-Kontorova model with impurities. , 1991, Physical review. B, Condensed matter.

[22]  Mobility and reactivity of discrete breathers , 1997, cond-mat/9712046.