What I want to say here is related to user1504's comment.

As Lenny Susskind explains in this and this lecture, how to describe the scattering behavior of particles is nearly the definition of string theory. So formulas for scattering amplitudes can in some way be considered as fundamental equations defining the theory. Very schematically, the equation to calculate the scattering amplitude $A$ can be written down as

$$ A = \int\limits_{\rm{period}} d\tau \int\limits_{\rm{surfaces}} \exp^{-iS} \Delta X^{\mu}(\sigma,\tau)$$

Considering for example the process of two strings joining and splitting again, one has to integrate over all world sheets $\Delta X^{\mu}(\sigma,\tau)$ that start and end with two distinct strings. A second integral has to be done over all possible periods of time $d\tau$ the strings join. The action $S$ may for example be given by

$$ S = \int d\tau d\sigma \left[ \left( \frac{\partial X^{\nu}}{\partial\tau} \right)^2 - \left( \frac{\partial X^{\nu}}{\partial\sigma} \right)^2 \right] $$

The information about the incoming and outgoing particles themself is still missing in the first equation and has to be inserted by hand by including additional multiplicative factors (vertex operators)

$$ \prod\limits_j e^{ik_{j_\mu} X^{\mu}(z_j)}$$

These factors represent a particle with wave vector $k$, and $z$ is the location of injection (for example on the unit circle when conformally transforming the problem to the unit disk) over which has finally to be integrated too.