On exact solutions of the Schafer-Wayne short pulse equation: WKI eigenvalue problem

We consider a new equation recently found by Schafer and Wayne, hereafter named Schafer-Wayne short pulse equation (SWSPE), describing the propagation of an ultrashort pulse in nonlinear media. Using some vanishing boundary conditions, we construct and discuss the N-soliton solutions to the previous equation by means of the Wadati-Konno-Ichikawa (WKI) method, which is arguably more direct than the map through the sine-Gordon equation investigated much earlier by Sakovich and Sakovich ( 2005 J. Phys. Soc. Japan 74 239, 2006 J. Phys. A: Math. Gen. 39 L361). We particularly focus our attention on the two-soliton solution as an application. As a result, the collision process for two-soliton solutions with 'similar' amplitudes are 'dissimilar'.