  The multi-peak solitons and their stability are investigated for the nonlocal
nonlinear system with the sine-oscillation response, including both the cases
of positive and negative Kerr coefficients. The Hermite-Gaussian-type
multi-peak solitons and the ranges of the degree of nonlocality within which
the solitons exist are analytically obtained by the variational approach. This
is the first time, to our knowledge at least, to discuss the solution existence
range of the multi-peak solitons analytically, although approximately. The
variational analytical results are confirmed by the numerical ones. The
stability of the multi-peak solitons are addressed by the linear stability
analysis. It is found that the upper thresholds of the peak-number of the
stable solitons are five and four for the system with negative and positive
Kerr coefficients, respectively.
