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.

Automated summary

In this paper, we investigate rational and semi-rational solutions to the third-type Davey-Stewartson (DS III) equation and its nonlocal version using Hirota's bilinear method and long wave limit technique. Rational solutions to the DS III equation include kinks, lumps, and line rogue waves, while semi-rational solutions exhibit hybrids of solitons, lumps, and line rogue waves. For the nonlocal DS III equation, we obtain (semi-)rational solutions and breather solutions, which show lumps on periodic line backgrounds, hybrids of breathers and lumps, line rogue waves, and line breathers on periodic line backgrounds.