Dark-bright quadratic solitons with a focusing effective Kerr nonlinearity

Dark solitons are traditionally considered to exist in defocusing Kerr nonlinearity media. We investigate dark quadratic solitons with a focusing effectiveKerr nonlinearity and a sine-oscillatory nonlocal response. Anonlinear refractive index with a focusing sine-oscillatory response leads to a defocusing effect with a strong degree of nonlocality, which causes the formation of dark solitons. By analyzing the modulational instability, we determine the parameter domain for dark quadratic solitons with a stable background and numerically obtain dark-bright soliton solutions in the form of pairs, which avoid radiative phenomena. Based on a numerical simulation, we find that all dark-bright soliton pairs are unstable after a relatively long propagation distance, and their stabilities are affected by the soliton interval and the degree of nonlocality.