The 3+1 Dimensional Toda Equation and its Exact Solutions

抄録

Exact solutions of the 3+1 dimensional Toda equation, Δ log V_n−V_n+1+2V_n−V_n−1=0, where Δ≡∂²⁄∂x²+∂²⁄∂y²+∂²⁄∂z² have been obtained. The boundary condition is the “molecule” condition which is vanishing V_n at both ends of the finite chain, V_N=V_−N=0 or V_N=V_−N−1=0. In the large molecule and small angle limit, the present solution reduces to the 2+1 dimensional cylindrical Toda soliton.