Multicomponent integrable wave equations: II. Soliton solutions

The Darboux-dressing transformations developed in Degasperis and Lombardo ( 2007 J. Phys. A: Math. Theor. 40 961–77 ) are here applied to construct soliton solutions for a class of boomeronic-type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one-soliton solutions. The formulae are specialized to the particularly interesting case of the resonant interaction of three waves, a well-known model which is of boomeronic type. For this equation a novel solution which describes three locked dark pulses (simulton) is introduced.