Relation Between Certain Quasi-Vortex Solutions and Solitons of the Sine-Gordon Equation and Other Nonlinear Equations

It is shown that the quasi-vortex type solutions recently studied by Hudak of the sine-Gordon equation, u x x + u y y =sin u , can be derived from the known multiple soliton solutions by the proper procedure. This shows in principle the existence of the multiple quasi-vorte solutions. It also shows that the superposition of usual solitons and quasi-vortex solutions are possible for this equation. Implication of the present results to other soliton equations is briefly discussed.