\شماره٪٪۱
Dietrich, WE., Wilson, CJ., Montgomery, DR. and et al. ``Analysis
of erosion thresholds, channel networks, and landscape morphology
using a digital terrain model'', {\it The Journal of Geology},
{\bf 101}(2), pp.259-78
(1993).
\شماره٪٪۲
Montgommery, D. and Foufoula-Georgiou, E. ``Channel network source
representation using digital elevation model'', {\it Water resources
research}, {\bf 29}, pp. 3925-34 (1993).
\شماره٪٪۳
Tarboton, DG., Bras, RL. and Rodriguez-Iturbe, I. ``On the extraction
of channel networks from digital elevation data'', {\it Hydrological
Processes}, {\bf 5}(1), pp. 81-100 (1991).
\شماره٪٪۴
Campbell, RE., Winterbourn, MJ., Cochrane, TA. and
et al. ``Flow-related
disturbance creates a gradient of metacommunity types within
stream networks'', {\it Landscape Ecology}, {\bf 30}(4), pp. 667-80 (2015).
\شماره٪٪۵
Lazzaro, G., Soulsby, C., Tetzlaff, D. and et al. ``A probabilistic
approach to quantifying hydrologic thresholds regulating migration
of adult Atlantic salmon into spawning streams'', {\it Water Resources
Research}, {\bf 53}(3), pp. 2264-77 (2017).
\شماره٪٪۶
Sarremejame, R., Ca\~{n}edo-Arg\"{u}elles, M., Part, N. and et al.
``Do metacommunities vary through time? Intermittent
rivers as model systems'', {\it Journal of Biogeography}, {\bf 44}(12),
pp. 2752-63
(2017).
\شماره٪٪۷
Dong, B., Ni, D. and Wang, Y. ``Sharing a polluted river network'',
{\it Environmental and Resource Economics}, {\it 53}(3), pp. 367-87 (2012).
\شماره٪٪۸
Leibundgut, C., Maloszewski, P. and K\"{u}lls, C. ``Tracers in hydrology '',
{\it John Wiley} \& {\it Sons}, p.432 (2011).
\شماره٪٪۹
Zhang, M-l., Shen, Y-m. and Guo, Y. ``Development and application
of a eutrophication water quality model for river networks'',
{\it Journal of Hydrodynamics}, {\bf 20}(6), pp. 719-26 (2008).
\شماره٪٪۱۰
Heaton, LL., L\'{o}pez, E., Maini, PK. and et al. ``Advection,
diffusion, and delivery over a network'', {\it Physical Review E},
{\bf 86}(2), pp. 021905 (2012).
\شماره٪٪۱۱
Guerrero, JP., Pimentel, LCG., Skaggs, TH. and et al. ``Analytical
solution of the advection--diffusion transport equation using
a change-of-variable and integral transform technique'', {\it International
Journal of Heat and Mass Transfer}, {\bf 52}(13-14), pp. 3297-304 (2009).
\شماره٪٪۱۲
Park, E. and Zhan, H. ``Analytical solutions of contaminant transport
from finite one-, two-, and three-dimensional sources in a finite-thickness
aquifer'',
{\it Journal of contaminant hydrology}, {\bf 53}(1-2), pp. 41-61 (2001).
\شماره٪٪۱۳
Wang, H. and Wu, H. ``Analytical solutions of three-dimensional
contaminant transport in uniform flow field in porous media'',
{\it A library Frontiers of Environmental Science} \& {\it Engineering in
China}, {\bf 3}(1), pp. 112-28 (2009).
\شماره٪٪۱۴
Leij, FJ. and Van Genuchten, MT. ``Analytical modeling of nonaqueous
phase liquid dissolution with Green's functions'', {\it Transport
in Porous Media}, {\bf 38}(1), pp. 141-66 (2000).
\شماره٪٪۱۵
Sanskrityayn, A., H. Suk, and N. Kumar, ``Analytical solutions
for solute transport in groundwater and riverine flow using Green's
function method and pertinent coordinate transformation method'',
{\it Journal of hydrology}, {\bf 547}, pp. 517-533 (2017).
\شماره٪٪۱۶
Sanskrityayn, A., et al. ``Analytical solution of two-dimensional
advection--dispersion equation with spatio-temporal coefficients
for point sources in an infinite medium using Green's function
method'', {\it Environmental Fluid Mechanics}, {\bf
18}(3), pp. 739-757 (2018).
\شماره٪٪۱۷
Mashhadgarme, N., Mazaheri, M. and Mohammad Vali Samani, J., ``Analytical
solutions to one-and two-dimensional Advection-Dispersion-Reaction
equation with arbitrary source term time pattern using Green's
function method'', {\it Sharif Journal of Civil Engineering}, {\bf 33-2},
pp. 77-91 (in Persian) (2017).
\شماره٪٪۱۸
Leij, FJ., Toride, N. and Van Genuchten, MT. ``Analytical solutions
for non-equilibrium solute transport in three-dimensional porous
media'', {\it Journal of Hydrology}, {\bf 151}(2-4), pp. 193-228 (1993).
\شماره٪٪۱۹
Cotta, R.M., Knupp, D.C. and Naveira-Cotta, C.P. ``Analytical
heat and fluid flow in microchannels and microsystems'', {\it Springer}, p.175
(2016).
\شماره٪٪۲۰
Adrian, DD, Yu, FX .and Barbe, D. ``Water quality modeling for a
sinusoidally varying waste discharge concentration'', {\it Water Research},
{\bf 28}(5), pp. 1167-74 (1994).
\شماره٪٪۲۱
Dresnack, R. and Dobbins WE. ``Numerical analysis of BOD and DO
profiles'', {\it Journal of the Sanitary Engineering Division},
{\bf 94}(5), pp. 789-808
(1968).
\شماره٪٪۲۲
Yu. F., Adrian, D. and Singh, V. ``Modeling river quality by the superposition
method'', {\it Journal of Environmental Systems}, {\bf 20}(4),
pp. 1-16 (1991).
\شماره٪٪۲۳
Chen, J-S., Liu, C-W., Liang, C-P. and et al. ``Generalized analytical
solutions to sequentially coupled multi-species advective--dispersive
transport equations in a finite domain subject to an arbitrary
time-dependent source boundary condition'', {\it Journal of hydrology},
{\bf 456}, pp. 101-9 (2012).
\شماره٪٪۲۴
Guerrero, JP. and Skaggs, T. ``Analytical solution for one-dimensional
advection--dispersion transport equation with distance-dependent
coefficients'', {\it Journal of Hydrology}, {\bf 390}(1-2), pp. 57-65 (2010).
\شماره٪٪۲۵
Bharati, VK., Singh, VP., Sanskrityayn, A. and et al. ``Analytical
solution for solute transport from a pulse point source along
a medium having concave/convex spatial dispersivity within fractal
and Euclidean framework'', {\it Journal of Earth System Science},
{\bf 128}(8), pp. 1-19
(2019).
\شماره٪٪۲۶
Shukla, V. ``Analytical solutions for unsteady transport dispersion
of nonconservative pollutant with time-dependent periodic waste
discharge concentration'', {\it Journal of Hydraulic Engineering},
{\bf 128}(9), pp. 866-9 (2002).
\شماره٪٪۲۷
Yang, S., Zhou, H., Zhang, S. and et al. ``Analytical solutions of
advective--dispersive transport in porous media involving conformable
derivative'', {\it Applied Mathematics Letters}, {\bf 92}, pp. 85-92 (2019).
\شماره٪٪۲۸
Xu, Z. and Meakin, P. ``Upscaling of solute transport in heterogeneous
media with non-uniform flow and dispersion fields'', {\it Applied
Mathematical Modelling}, {\bf 37}(18-19), pp. 8533-42 (2013).
\شماره٪٪۲۹
Simpson, MJ. and Ellery, AJ. ``Exact series solutions of reactive
transport models with general initial conditions'', {\it Journal of
Hydrology}, {\bf 513}, pp. 7-12 (2014).
\شماره٪٪۳۰
Williams, GP. and Tomasko, D. ``Analytical solution to the advective-dispersive
equation with a decaying source and contaminant'', {\it Journal of
Hydrologic Engineering}, {\bf 13}(12), pp. 1193-6 (2008).
\شماره٪٪۳۱
Kumar, P. and Sudheendra, S. ``Mathematical solution of transport
of pollutant in unsaturated porous media with retardation factor'',
{\it International Journal of Applied Engineering Research}, {\bf 13}(1),
pp. 100-4 (2018).
\شماره٪٪۳۲
Chen, J.-S., et al. ``Analytical model for advective-dispersive
transport involving flexible boundary inputs, initial distributions
and zero-order productions'', {\it Journal of Hydrology}, {\bf 554},
pp. 187-199
(2017).
\شماره٪٪۳۳
Carr, E.J. ``New semi-analytical solutions for advection--dispersion
equations in multilayer porous media'', {\it Transport in Porous Media},
{\bf 135}(1), pp. 39-58 (2020).
\شماره٪٪۳۴
Yadav, R. and Kumar, L. ``Solute transport for pulse type input
point source along temporally and spatially dependent flow'',
{\it Pollution}, {\bf 5}(1), p. 53-70 (2019).
\شماره٪٪۳۵
Yadav, R. and Yadav, V. ``Three-dimensional analytical models
for time-dependent coefficients through uniform and varying plane
input source in semi-infinite adsorbing porous media'', {\it Pollution},
{\bf 5}(1), pp. 81-98 (2019).
\شماره٪٪۳۶
Genuchten, MT., Leij, FJ., Skaggs, TH. and et
al.
``Exact analytical solutions for contaminant transport in
rivers 1. The equilibrium advection-dispersion equation'', {\it Journal
of Hydrology and Hydromechanics}, {\bf 61}(2), pp. 146 (2013).
\شماره٪٪۳۷
Mazaheri, M., MV Samani, J. and Samani H. ``Analytical solution
to one-dimensional advection-diffusion equation with several
point sources through arbitrary time-dependent emission rate
patterns'', {\it Journal of Agricultural Science and Technology},
{\bf 15}(6):1231-45
(2013).\\
\شماره٪٪۳۸
Kumar, A., Jaiswal, DK. and Kumar, N. ``Analytical solutions of one-dimensional
advection-diffusion equation with variable coefficients in a
finite domain'', {\it Journal of Earth System Science},
{\bf 118}(5), pp. 539-49
(2009).
\شماره٪٪۳۹
Yates, SR. ``An analytical solution for one-dimensional transport
in heterogeneous porous media'', {\it Water Resources Research},
{\bf 26}(10), pp. 2331-8
(1990).
\شماره٪٪۴۰
Bavandpouri Gilan, N., Mazaheri, M. and Fotouhi Firouzabadi, M. ``Analytical
solution of contaminant transport equation in river by arbitrary
variable coefficients using generalized integral transform technique'',
{\it Journal of Advanced Mathematical Modeling}, {\bf 7}(1), pp. 89-116
(in Persian) (2017).
\شماره٪٪۴۱
Mashhadgarme, N., Mohammadvali Samani, J. and Mazaheri, M. ``Analytical
solution of pollution transport equation with arbitrary time
pattern of multiple point sources using Green's function method'',
{\it Journal of Hydraulics}, {\bf 8}(4), pp. 13-25 (in Persian) (2013).
\شماره٪٪۴۲
Ramezani M., et al. ``Numerical modelling-based comparison of
longitudinal dispersion coefficient formulas for solute transport
in rivers'', {\it Hydrological Sciences Journal}, {\bf 64}(7), pp. 808-819
(2019).
\شماره٪٪۴۳
Najafzadeh, M. et al. ``A comprehensive uncertainty analysis
of model-estimated longitudinal and lateral dispersion coefficients
in open channels'', {\it Journal of Hydrology}, {\bf 603}, pp. 126850 (2021).
\شماره٪٪۴۴
Noori, R. et al. ``Estimation of the dispersion coefficient
in natural rivers using a granular computing model'', {\it Journal
of Hydraulic Engineering}, {\bf 143}(5), pp. 04017001 (2017).
\شماره٪٪۴۵
Korn, GA. and Korn, TM. ``Mathematical handbook for scientists and
engineers: definitions, theorems, and formulas for reference
and review'', {\it Courier Corporation}, p.1152 (2000).
\شماره٪٪۴۶
Horv\'{a}th, G., Horv\'{a}th, I., Almousa, SA-D. and et al. ``Numerical inverse
laplace transformation using concentrated matrix exponential
distributions'', {\it Performance Evaluation}, {\bf 137}, pp. 102067 (2020).
\شماره٪٪۴۷
Stehfest, H. ``Algorithm 368: Numerical inversion of Laplace transforms
[D5]'', {\it Communications of the ACM}, {\bf 13}(1), pp. 47-9 (1970).
\شماره٪٪۴۸
Villinger, H. ``Solving cylindrical geothermal problems using
the Gaver-Stehfest inverse Laplace transform'', {\it Geophysics},
{\bf 50}(10), pp. 1581-7
(1985).
\شماره٪٪۴۹
Murli, A. and Rizzardi, M. ``Algorithm 682: Talbot's method of
the Laplace inversion prob