Dynamics of surface dipole and tripole solitons in nonlocal nonlinear media with optical lattice field

•We study surface soliton in a nonlocal nonlinear medium with an optical lattice field.•The existence conditions for new stationary dipole and tripole surface solitons are found.•The stability of the surface solitons is investigated.•The relationship between the power and the model parameters for stable solitons is identified.

We find the existence conditions for stationary dipole and tripole surface solitons formed at the interface of a nonlocal nonlinear medium and a lattice with linearly modulated frequency. We investigate how the degree of nonlocality, the depth, and the modulation frequency of the optical lattice field affect on the existence of the surface solitons and their dynamics. The relationship between the power and the model parameters is identified. The stability of the surface dipole and tripole solitons is numerically investigated.