CUSP Solitons to the Long-Short Waves Equation and the ∂¯-Dressing Method

The dressing method based on 3 × 3 matrix ∂ ¯ -problem is extended to study the long-short waves equation with the cases σ = ±1. The soliton solutions for the long-short wave equation for σ = ±1 are given by means of the properties of Cauchy matrix. It is shown that the long-short wave equation for σ = 1 has the cusp solitons.