Traveling waves and compactons in phase oscillator lattices.

We study waves in a chain of dispersively coupled phase oscillators. Two approaches--a quasicontinuous approximation and an iterative numerical solution of the lattice equation--allow us to characterize different types of traveling waves: compactons, kovatons, solitary waves with exponential tails as well as a novel type of semicompact waves that are compact from one side. Stability of these waves is studied using numerical simulations of the initial value problem.

[1]  H. Jürgensen.  Synchronization , 2021, Inf. Comput..

[2]  Monika Sharma,et al.  Chemical oscillations , 2006 .

[3]  Philip Rosenau,et al.  Phase compactons , 2006 .

[4]  Arkady Pikovsky,et al.  Phase compactons in chains of dispersively coupled oscillators. , 2005, Physical review letters.

[5]  M. M. Smirnov,et al.  PROPAGATION OF NONLINEAR COMPRESSION PULSES IN GRANULAR MEDIA , 2004 .

[6]  Arkady Pikovsky,et al.  Reversibility vs. synchronization in oscillator lattices , 2002 .

[7]  L. Glass.  Synchronization and rhythmic processes in physiology , 2001, Nature.

[8]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[9]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[10]  D. V. Vysotsky,et al.  Phase locking in a multicore fiber laser by means of a Talbot resonator. , 2000, Optics letters.

[11]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[12]  G. Bard Ermentrout,et al.  Phase locking in chains of multiple-coupled oscillators , 2000 .

[13]  Alwyn C. Scott,et al.  Nonlinear Science: Emergence and Dynamics of Coherent Structures , 1999 .

[14]  C. R. Willis,et al.  Discrete Breathers , 1997, patt-sol/9704004.

[15]  P. Rosenau,et al.  Nonlinear dispersion and compact structures. , 1994, Physical review letters.

[16]  S. Strogatz,et al.  Constants of motion for superconducting Josephson arrays , 1994 .

[17]  S. Strogatz,et al.  Integrability of a globally coupled oscillator array. , 1993, Physical Review Letters.

[18]  Hyman,et al.  Compactons: Solitons with finite wavelength. , 1993, Physical review letters.

[19]  S. Strogatz,et al.  Splay states in globally coupled Josephson arrays: Analytical prediction of Floquet multipliers. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  H. Daido,et al.  Order Function and Macroscopic Mutual Entrainment in Uniformly Coupled Limit-Cycle Oscillators , 1992 .

[21]  Nichols,et al.  Ubiquitous neutral stability of splay-phase states. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[22]  Daido,et al.  Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions. , 1992, Physical review letters.

[23]  S. Strogatz,et al.  Dynamics of a globally coupled oscillator array , 1991 .

[24]  Shigeru Shinomoto,et al.  Mutual Entrainment in Oscillator Lattices with Nonvariational Type Interaction , 1988 .

[25]  G. Ermentrout,et al.  Symmetry and phaselocking in chains of weakly coupled oscillators , 1986 .

[26]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[27]  G. Ermentrout,et al.  Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I. , 1984 .

[28]  S. Kulikov,et al.  Experimental check on a theoretical model for a CO2 GDL based on combustion products at high stagnation temperatures , 1982 .

[29]  V. Petviashvili.  Multidimensional and dissipative solitons , 1981 .

[30]  Yoshiki Kuramoto,et al.  Self-entrainment of a population of coupled non-linear oscillators , 1975 .

[31]  Huzihiro Araki,et al.  International Symposium on Mathematical Problems in Theoretical Physics , 1975 .