On multisoliton solutions of the constant astigmatism equation

We introduce an algebraic formula producing infinitely many exact solutions of the constant astigmatism equation $z_{yy}+(1\mathrm{/}z{)}_{xx}+2=0$ from a given seed. A construction of corresponding surfaces of constant astigmatism is then a matter of routine. As a special case, we consider multisoliton solutions of the constant astigmatism equation defined as counterparts of famous multisoliton solutions of the sine-Gordon equation. A few particular examples are surveyed as well.