The quasi-line soliton: Solutions to the Davey-Stewartson I equation

[Abstract] A periodic soliton is turned into a line soliton accordingly as a parameter point approaches to the boundary of the existing domain in the parameter space for a non-singular periodic soliton solution. We will call the periodic soliton solution with parameters of the neighborhood of the boundary a quasi-line soliton in this paper. We will examine that a periodic soliton turn into the line soliton as the parameter point of a periodic soliton approaches to the neighborhood of the boundary