2018/08/22 by Emmanuel Garza, Servando López-Aguayo, Servando Lopez-Aguayo +1
Computer Science · Mathematics · Physics and Astronomy · #Bifurcation #Bifurcation theory #Boundary (topology) #Boundary value problem #Classical mechanics #Dynamics (music) #Geometry #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pitchfork bifurcation #Quantum entanglement #Quantum mechanics #Quantum nonlocality #Refractive index #Soliton #Symmetry (geometry) #nlin.PS #physics.optics
paper · pdf · doi:10.1103/physreva.99.033804
published as Phys. Rev. A 99, 033804 (2019)
arxiv created 2018/08/22 · openalex publication_date 2019/03/01 · arxiv updated 2019/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The effect of finite boundaries in the propagation of spatial nonlocal solitons in media with cylindrical symmetry is analyzed. Using Ehrenfest's theorem together with the Green's function of the nonlinear refractive index equation, we derive an analytical expression for the force exerted on the soliton by the boundaries, verifying its validity by full numerical propagation. We show that the dynamics of the soliton are determined not only by the degree of nonlocality, but also by the boundary conditions for the refractive index. In particular, we report that a supercritical pitchfork bifurcation appears when the boundary condition exceed a certain threshold value.