The 3+1 Dimensional Toda Equation and its Exact Solutions

Abstract

Exact solutions of the 3+1 dimensional Toda equation, Δlog V n - V n +1 +2 V n - V n -1 =0, where Δ≡∂ 2 /∂ x 2 +∂ 2 /∂ y 2 +∂ 2 /∂ z 2 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.