Breather collisions: A survey of recent results

Discrete breathers collisions: An overview and some recent results Jesús Cuevas Maraver Nonlinear Physics Group Universidad de Sevilla Outline Overview of previous studies: Collisions in FPU lattices Collisions in dissipative Klein–Gordon lattices Collisions in DNLS lattices New results on DNLS lattices with saturable nonlinearity: Properties of SDNLS lattices Collisions in SDNLS lattices Future challenges Discrete Breathers collisions: An overview and some recent results – p.1/16 FPU lattices Y. Doi, PRE 68, 066608 (2003) β-FPU model is considered Collisions of breathers with the same/different energies and the same/different phase Observed regimes: Reflection Fusion Symmetry breaking (even if same energy and same phase) The energy exchange is throughoutly studied Transferred energy may be very sensitive to phase difference Discrete Breathers collisions: An overview and some recent results – p.2/16 FPU lattices Fusion and symmetry breaking regimes Discrete Breathers collisions: An overview and some recent results – p.3/16 Dissipative Klein-Gordon lattices M. Meister & L.M. Floría, EPJB 37, 213 (2004) Frenkel–Kontorova model with dissipation and external force Collisions of breathers with the same energy and phase Observed regimes: Reflection Destruction of one/both breathers Bound state: Pair of breathers subject to the force of the emitted phonons The distance between breathers is related to the velocity The final states are attractors of the system Discrete Breathers collisions: An overview and some recent results – p.4/16 Dissipative Klein-Gordon lattices Different regimes Discrete Breathers collisions: An overview and some recent results – p.5/16 Dissipative Klein-Gordon lattices A bound state Discrete Breathers collisions: An overview and some recent results – p.6/16 Nonintegrable DNLS lattices I.E. Papacharalampous et al, PRE 68, 046604 (2003) Collisions of breathers with the same energy and the same/different phase Observed regimes (in-phase breathers): Reflection Bound state Spontaneous symmetry breaking (due to numerical errors): Bound state moves with a well-defined value of the velocity Mutual bounce after multiple collisions High Peierls-Nabarro barrier →Strong differences between on-site and inter-site collisions. Discrete Breathers collisions: An overview and some recent results – p.7/16 Nonintegrable DNLS lattices Several regimes Discrete Breathers collisions: An overview and some recent results – p.8/16 Collisions in SDNLS lattices Velocity difference (Incoming-Outgoing) 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 P ∆ v 0 50 100 0.1 0.15 0.2 0.25 P <∆ v> 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 P ∆ V 0 50 100 0.1 0.15 0.2 0.25 0.3 0.35 P <∆ v> Inter-site collisions On-site collisions Discrete Breathers collisions: An overview and some recent results – p.15/16 Conclusions In all cases, reflection and bound state formation is observed Symmetry breaking is also observed, with different origins: DNLS: Numerical errors Dissipative KG: Attractor of the system FPU: Unexplained Saturable nonlinearity allows high-power breathers Future challenge: Study the case of Hamiltonian Klein-Gordon lattices. Discrete Breathers collisions: An overview and some recent results – p.16/16