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 onesoliton 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.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 2009|