Explicit solutions to Poncelet’s porism

Explicit multiple singular periodic solutions and singular soliton solutions to KdV equation

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

A Proof of White's Porism.

It is interesting to find that the lithium lines X4602 and X4132 show polarized components in the longitudinal effect. The longitudinal effects in hydrogen and helium, the only ones investigated up to this time, had given unpolarized components. Previously, only the diffuse series of elements had shown large electric effects which makes the calcium results most unexpected. H and K belong to a p...

explicit multiple singular periodic solutions and singular soliton solutions to kdv equation

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...

Explicit Solutions for Queueing Problems

Explicit exact solutions for variable coefficient Broer-Kaup equations

Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient Broer-Kaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient Broer...