Analytical Solutions to the Problem of Natural Attenuation.

Analytical solutions to the one-dimensional solute transport equation are revisited.  Known exact solutions of the equation for a constant source are expanded and their asymptotic forms are given  for different ranges of parameters.   A generic solution, a solution for a generic source configuration,  is written using the principle of superposition. An arbitrary time-dependent source is approximated by a step-functional source making it locally constant. The properties of this generic solution are studied. Its approximations are written in the limited cases.  Using an analytical approximation to the error function, the properties of the solution are studied graphically.  A general approach to groundwater contamination study is proposed using our new solution. The future development of the ideas presented in the paper are outlined.  An example is given to illustrate the method developed in this paper.