Impact of nonlocality and quintic local nonlinearity on the pulses interaction and the dynamical characteristics parameters of soliton in weakly nonlinear nonlocal media

•We investigate analytically and numerically the nonlinear Schrödinger equation which describes the dynamics of pulses in a cubic nonlocal and quintic local nonlinearities.•Using variational method, we have brought out the variational equations which describe the behaviors of the internal parameters of the pulses.•We show the action mode of propagation parameters on the pulse internal parameters.•Numerical simulation allowed us to conclude on the impact of quintic nonlinearity and nonlocality on the pulse behaviors. We study the impact of nonlocality and local quintic nonlinearity on the dynamic characteristic parameters of spatial optical bright soliton and on their interaction and collision in weakly nonlocal nonlinear media. For this purpose, we establish the propagation equation governing this dynamic which is a nonlinear cubic-quintic Schrödinger equation. We approach the solution of this equation by a secant hyperbolic ansatz. By the means of the variational method, we bring out the action mode of the nonlocality and quintic nonlinearity on the pulse parameters. Subsequently, a numerical analysis is made and allows us to conclude on their role on the dynamic of pulse in these media. It follows that quintic nonlinearity contributes to the pulse compression and the increase of phase-front curvature, while nonlocality participates in enlargement and the decrease of the phase-front curvature. Taking into account the two effects helps stabilize the soliton during its propagation by generating a new dynamic state depending on whether the quintic nonlinearity and the nonlocality add up, compensate each other, or that one of the two effects is more important than the other. Concerning their interaction, we showed that quintic nonlinearity provides a repulsive force when nonlocality provides an attractive force. In the case of collision, quintic nonlinearity can induce elastic or inelastic collision.