On multisoliton solutions of the constant astigmatism equation

Adam Hlaváč
2015 Journal of Physics A: Mathematical and Theoretical  
We introduce an algebraic formula producing infinitely many exact solutions of the constant astigmatism equation $ z_{yy} + ({1}/{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.
doi:10.1088/1751-8113/48/36/365202 fatcat:uqitklfvonbyzdydjp7wv5hi4i