Fig. 2: Nonlocal nonlinear soliton solutions considering a second-order nonlinear term.
From: Nonlinear optical simulation of the post-Newton Schrödinger equation
Upper panel: Theoretical existence curve for soliton with nonlocal change of the refractive index. FWHM of the solitons vs. power, for Newtonian-type (γ2 = 0 in Eq. (1)) and Post-Newtonian type (γ2 = −3.43 ⋅ 10−6 in Eq. (1)) potentials. Inset shows the soliton spatial profile. Lower: Eigenvalues \(\left(\Gamma \right)\) of solitons vs optical power for Newtonian and post-Newtonian potentials. For the numerical solution we set the following physical parameters: λ = 532 nm, γ1 = 14 ⋅ 10−61/K, κ = 0.7W/(mK), α = 0.01 cm−1, L = 4 mm being the length of the rectangular boundary. For proof of convergence of the soliton solutions presented see Supplemantery Materials, section 2.
