부산대학교 도서관

Authors' summary: ``We study the propagation and the interaction of cylindrical solitons in shallow water of variable depth. Starting from the cylindrically symmetric version of the equations describing long waves on a beach, a Korteweg-de Vries type equation $\psi_\tau+6\psi\psi_\xi+\psi_{\xi\xi\xi}=-\Gamma(\tau)\psi$ is derived. Since no exact analytical solution has been found to date for this equation, some remarkable cases in which the equation takes on a tractable form are analysed. Finally the interaction between cylindrical imploding and expanding waves is considered and the phase shifts caused by a head-on collision are given.''