Supernova remnant RX J1713.7-3946 (also named as G347.3-0.5) has exhibited largest surface brightness, detailed spectral and shell-type morphology, it is one of the brightest TeV sources. The recent H.E.S.S. observation of RX J1713.7-3946 revealed textbf{a} broken power-law spectrum of GeV-TeV gamma-ray spectrum and more extended gamma-ray spatial radial profile than that in the X-ray band. Based on the diffusion shock acceleration model, we solve spherically symmetric hydrodynamic equations and transport equations of particles, and investigate multi-band non-thermal emission of RX J1713.7-3946 and radial profiles of its surface brightness for two selected zones in the leptonic scenario for the $gamma$-ray emission. We found (1) the diffusion coefficient has a weak energy-dependent, and the Kolmogorov type is favored; (2) the magnetic field strength could vary linearly or nonlinearly with radius for different surrounding environments because of possible turbulence in shock downstream region, and a compressional amplification is likely to exist at the shock front; (3) the non-thermal photons from radio to X-ray bands are dominated by synchrotron emission from relativistic electrons, if the GeV-TeV gamma-rays are produced by inverse Compton scattering from these electrons interacting with the background photons, then the X-ray and gamma-ray radial profiles can be reproduced except for the more extended $gamma$-ray emission.
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