  In our model, the acceleration and propagation of particles from the
Bohm-like diffusion region inside the SNR to the Galactic diffusion region
outside the SNR are described through nonlinear diffusive shock acceleration
(NLDSA). The main content of our NLDSA model is to solve the hydrodynamic
equations numerically for gas density, gas velocity, gas pressure as well as
the equation for the quasi-isotropic particle momentum distribution. The
consequent multi-band non-thermal emission is from two different regions,
namely the acceleration region and the escaping region. Our model is capable of
explaining the multi-band photon emission via the dominant synchrotron
radiation of the electrons accelerated inside the SNR; and the photons with
energy of $\gtrsim$ GeV are naturally produced by the protons inside and
outside the SNR. Moreover, the photons in the energy range of $\sim 1 - \sim
100$ TeV are due to the interaction of escaped protons with dense molecular
clouds. For the photons with energy of $E_\gamma \gtrsim $ 1 GeV from SNR
G106.3+2.7, our results here favor a hadronic origin, where the photons in the
energy range of $\sim 1$ GeV to $\sim 1$ TeV are produced inside the SNR
through proton-proton interaction, while the photons with $E_\gamma \gtrsim 1$
TeV originate from the interaction of escaped protons with a dense molecular
cloud.
