2015/08/12 by Jennie D’Ambroise, J. D'Ambroise, M. Salerno +3 · 9 citations
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Antisymmetric relation #Bessel function #Classical mechanics #Instability #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear Waves and Solitons #Nonlinear system #Parametric statistics #Physics #Quantum mechanics #Statistical physics #Vortex #cond-mat.quant-gas #nlin.PS
paper · pdf · doi:10.1103/physreva.92.053621
published in Physical Review A 92(5) (American Physical Society)
arxiv created 2015/08/12 · openalex publication_date 2015/11/19 · arxiv updated 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The existence of multidimensional lattice compactons in the discrete nonlinear Schr"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined. Other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. The possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.