Soliton solutions to the nonlocal Davey–Stewartson III equation

Abstract

The soliton solutions on both constant and periodic backgrounds of the nonlocal Davey–Stewartson III equation are derived by using the bilinear method and the Kadomtsev-Petviashvili (KP) hierarchy reduction method. These solutions are presented as [Formula: see text] Gram-type determinants, with [Formula: see text] a positive integer. Typical dynamics of these soliton solutions are investigated in analytical and graphical aspects. Two types of soliton solutions are generated with different [Formula: see text]. When [Formula: see text] is even, solitons on the constant background can be constructed, whereas solitons appear on the periodic background for odd [Formula: see text]. Under suitable parameter restrictions, we show the regularity of solutions and display all patterns of two- and four-soliton solutions.