Rational and semi-rational solutions to the Davey-Stewartson III equation

In this paper, based on the combination of Hirota’s bilinear method and long wave limit technique, we investigate rational and semi-rational solutions to the third-type Davey-Stewartson (DS III) equation and its nonlocal version. Rational solutions to the DS III equation demonstrate to be kinks, lumps and line rogue waves, while semi-rational solutions display hybrids of solitons, lumps and line rogue waves. As to the nonlocal DS III equation, we derive (semi-)rational solutions and breather solutions. Semi-rational solutions show lumps on the periodic line backgrounds, hybrids of breathers and lumps, line rogue waves and line breathers on the periodic line background.