Width of the Whitehead double of a nontrivial knot

In this paper, we prove that $w(K) =4w(J)$, where $w(.)$ is the width of a knot and $K$ is the Whitehead double of a nontrivial knot $J$.
Comment: 10 pages, 4 figures. In the new version, we re-draw all the figures and update the acknowledgement