Cusp solitons to the long-short waves equation and the $\bar\partial$-dressing method
arXiv:1406.6749 · doi:10.1016/S0034-4877(15)30003-3
Abstract
The dressing method based on $3\times3$ matrix $\bar{\partial}$-problem is extended to study the long-short waves equation with the cases $Ï=\pm1$. The soliton solutions for the long-short wave equation for $Ï=\pm1$ are given by means of the properties of Cauchy matrix. It is shown that the long-short wave equation for $Ï=1$ has the cusp solitons.
15 pages, 8figures