Abstract
Based on a modification of the method of the average Lagrangian, the influence of transverse perturbations on the breather of the sine-Gordon equation is investigated using the procedure of double averaging over the phase and group canonical variables. It is demonstrated that the transverse perturbations on the eikonal stage promote self-focusing of breathers. A criterion for determining conditions of suppression of self-focusing effect by diffraction is obtained. The breathers containing an arbitrary number of phase oscillations are examined.
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