Darboux transformation and bidirectional soliton solutions of a new (2+12+1)-dimensional soliton equation

A new (2+12+1)-dimensional soliton equation and its spectral problems are presented. The Darboux transformation with multi-parameters for the spectral problems is constructed with the help of a gauge transformation. And by using the Darboux transformation, some new bidirectional soliton solutions of the (2+12+1)-dimensional soliton equation are obtained. An interesting solution of three-peak soliton has been found.