  Context: We introduce the Dwarf Galaxy Survey with Amateur Telescopes (DGSAT)
project and report the discovery of eleven low surface brightness (LSB)
galaxies in the fields of the nearby galaxies NGC 2683, NGC 3628, NGC 4594
(M104), NGC 4631, NGC 5457 (M101), and NGC 7814. Aims: The DGSAT project aims
to use the potential of small-sized telescopes to probe LSB features around
large galaxies and to increase the sample size of the dwarf satellite galaxies
in the Local Volume. Methods: Using long exposure images, fields of the target
spiral galaxies are explored for extended low surface brightness objects. After
identifying dwarf galaxy candidates, their observed properties are extracted by
fitting models to their light profiles. Results: We find three, one, three,
one, one, and two new LSB galaxies in the fields of NGC 2683, 3628, 4594, 4631,
5457, and 7814, respectively. In addition to the newly found galaxies, we
analyse the structural properties of nine already known galaxies. All of these
20 dwarf galaxy candidates have effective surface brightnesses in the range
$25.3\lesssim\mu_{e}\lesssim28.8$ mag.arcsec$^{-2}$ and are fit with Sersic
profiles with indices $n\lesssim 1$. Assuming that they are in the vicinity of
the above mentioned massive galaxies, their $r$-band absolute magnitudes, their
effective radii, and their luminosities are in the ranges $-15.6 \lesssim M_r
\lesssim -7.8$, 160 pc $\lesssim R_e \lesssim$ 4.1 kpc, and $0.1\times 10^6
\lesssim\left(\frac{L}{L_{\odot}}\right)_r\lesssim127 \times 10^6$,
respectively. To determine whether these LSB galaxies are indeed satellites of
the above mentioned massive galaxies, their distances need to be determined via
further observations. Conclusions: Using small telescopes, we are readily able
to detect LSB galaxies with similar properties to the known dwarf galaxies of
the Local Group.
