In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear equation f(x) = 0 by rewriting the given nonlinear equation as a coupled system of equations and using the Taylor series. It is shown that this new iterative method is of fifth-order. Several examples are given to illustrate its performance and efficiency. Comparison with other methods is also given. Thi...

We consider fifth-order nonlinear dispersive K(m,n, p) type equations to study the effect of nonlinear dispersion. Using simple scaling arguments we show, how, instead of the conventional solitary waves like solitons, the interaction of the nonlinear dispersion with nonlinear convection generates compactons the compact solitary waves free of exponential tails. This interaction also generates ma...

For a given nonzero bounded linear operator A on a Banach space X, we show that if A or A∗ has an eigenvalue then, except when the dimension of X is equal to two and the trace of A is zero, there exists a bounded linear operator B on X such that (i) AB + BA is of rank one, and (ii) I + f (A)B is invertible for every function f analytic in a neighborhood of the spectrum of A. This result was mot...