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On multisoliton solutions of the constant astigmatism equation

Adam Hlaváč

2015
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Journal of Physics A: Mathematical and Theoretical
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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