The semi-infinite system of nonlinear differential equations Ak=2Ak(Ak+1-Ak-1): methods of integration and asymptotic time behaviours

Abstract

Under the boundary condition on the initial value Ak(0)(>0; k=1, 2, .) that Ak(0) to 0(k to infinity ), the author integrates the semiinfinite system of nonlinear differential equations Ak=2Ak(Ak+1-Ak-1) (k=1, 2, .; A0=0) to obtain its general solution. He further investigates the asymptotic time behaviours of this general solution as t to +or- infinity . The relation between the method of integration in this paper and the one proposed previously, which relies on the finite continued fractions, is also elucidated.