Are there Soliton Solutions for Maxwell's Equations? Some non-linear differential equations (such as Korteweg–de Vries and Kadomtsev–Petviashvili equations) have "solitary waves" solutions (solitons).

Does the set of partial differential equations known as "Maxwell's equations" theoretically admit such kind of solutions?
In that case, should these solutions appear in the form of "stationary shells" of electromagnetic field? By "stationary", I mean do the solutions maintain their shape?

Thanks for your comments!
 A: Adrian has given an interesting answer already, but I think it is worth pointing out two key points which were necessary for his soliton situation. Firstly, it was necessary to impose some specific form of initial-boundary data (to constrain the waves to inside the fibre optic cable), and secondly it was necessary to impose physical assumptions on the medium which actually changed the underlying PDE.  
If one considers the source-free Maxwells equations in a vacuum, then you know that the electric and magnetic fields $E$ and $B$ satisfy the standard wave equations $\Box E=0$, $\Box B =0$. If you work on the domain $(x,t)\in \mathbb{R}^3 \times [0,\infty)$ of "open space", and if you pose a Cauchy problem for the equations, which means if you specify some initial data (which must of course satisfy divergence free conditions) along the initial surface $t=0$, then it follows from Kirchoff's formula for the solution that the fields $E$ and $B$ have to decay in time. Specifically, one has $\|D^\alpha E(\cdot,t), D^\alpha B(\cdot,t)\|_{L^\infty(\mathbb{R}^3)} \to 0$ as $t\to \infty$ where $D^\alpha$ represents any chosen choice of composition of partial derivatives. 
Thus solutions to Maxwell's equations on an unbounded domain must always "scatter at infinity", and you can't hope to find soliton type solutions.
A: The answer is yes to both questions. If you cast Maxwell's Equations in cylindrical coordinates for a fiber optic cable, and you take birefringence into account, you get the coupled nonlinear Schrödinger equations. You can then solve those by means of the Inverse Scattering Transform, which takes the original system of nonlinear pde's (nonlinear because of the coordinate system), transforms them into a coupled system of linear ode's (the Manakov system) which are straight-forward to solve, and then, by means of the Gel'fand-Levitan-Marchenko integral equation, you arrive at the soliton solutions of the original pde's. For references, see C. Menyuk, Application of multiple-length-scale methods to the study of optical fiber transmission, Journal of Engineering Mathematics 36: 113-136, 1999, Kluwer Academic Publishers, Netherlands, and my own dissertation, which includes other references of interest. In particular, Shaw's book Mathematical Principles of Optical Fiber Communication has most of these derivations in it. 
The resulting soliton solutions behave mostly like waves, but they also interact in a particle-like fashion; for example, in a collision, they can alter each others' phase - a decidedly non-wave-like behavior. Solitons do not stay in one place; in the case above, they would travel down the fiber cable (indeed, solitons are the reason fiber is the backbone of the Internet!), and self-correct their shape as they go. And, as Maxwell's equations are all about electromagnetic fields, the solutions are, indeed, stationary (in your sense) "shells" of electromagnetic fields.
