On multisoliton solutions of the constant astigmatism equation

Abstract

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.

21 pages, 9 figures

References in corpus (1)

• On integrability of Weingarten surfaces: a forgotten class

Cited by in corpus (3)

• More exact solutions of the constant astigmatism equation
• Nonlocal conservation laws of the constant astigmatism equation
• Rotational surfaces of constant astigmatism in space forms