Solving Pell’s equation is of relevance in finding fundamental units in real quadratic fields and for this reason polynomial solutions are of interest in that they can supply the fundamental units in infinite families of such fields. In this paper an algorithm is described which allows one to construct, for each positive integer n, a finite collection, {Fi}, of multi-variable polynomials (with ...

This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order ...