Computerized symbolic computation for the cylindrical Korteweg-de Vries equation

Computers have a great potential in the analytical investigations on various physics problems. In this paper, we make use of computerized symbolic computation to obtain two similarity reductions as well as a rational solution for the variable-coefficient cylindrical Korteweg-de Vries equation, which was originally introduced in the studies of plasma physics. One of the reductions is to the second Painlevé equation, while the other to either the first Painlevé equation or the Weierstrass elliptic function equation. Our results are in agreement with the Painlevé conjecture.