Analytical and Computational Studies of Resonance Width near the Intersection of Two Resonances

When the working point (¿x, ¿y) lies near the intersection of two sum resonances that arise from the same nonlinear multipole field, the width of each resonance is modified by the presence of the other. Taking the two third-integer resonances 3¿X= N and ¿X+ 2¿y= N as an example, we have developed an analytical treatment of this problem and its predictions have been compared with numerical results.