Stretching and Shrinking of the Loop Soliton Interacting with a External Field

The integrable equation of motion of the loop soliton interacting with an external field is considered from the standpoint of stretching and/or shrinking of the loop. To study the role of the elastic force and the nonlinear forces, the basic equation is divided into three equations. We obtain stationary solutions for these equations and numerically solve their initial value problems to seek stability of the loop soliton.