These include Lagergren first-order equation and pseudo-

second-order equation, Elovich equation, Bangham's equation and intra-particle diffusion equation.

In order to obtain solitary wave amplitude equation, we continue solving

second-order equation about e:

For each type of surface, the function in (1) turns out to be specified by a nonlinear

second-order equation. It will be shown finally that Lax pairs can subsequently be formulated for each of the two second-order systems.

For the

second-order equation, the half-release times range was between 5.64 * [10.sup.2] min and 9.96 * [10.sup.2] min.

But no one has discussed the general

second-order equation (1).

In addition, these two symbolic solutions are not required to be known explicitly but are onlyassumed to satisfythe

second-order equation. Infact, we have ultimately expressed the first integrals found solely in terms of q, y and their derivatives.

These kinetic models included the pseudo first-order equation, the pseudo

second-order equation and the Elovich equation.

We first introduce an auxiliary variable [gamma] = -[nabla] x (a(t)[nabla]u) to reduce the fourth-order parabolic equation to a coupled system of

second-order equations, then solve a

second-order equation by FE method.

Figure 3 shows conversion rate predicted basing on the

second-order equation and variable order calculated by Eq.

The sorption process could be best described by the

second-order equation.

can be transformed into a

second-order equation (Eq.

However, in our previous research [20] we found that the boundary value problems with the

second-order equation cannot tackle the beginning stage of pipeline lifting and the ending stage of pipeline lowing accurately.