General high-order solitons and breathers with a periodic wave background in the nonlocal Hirota–Maccari equation

Soliton and breather solutions to the nonlocal Hirota–Maccari equation with a periodic wave background are constructed via the KP hierarchy reduction approach. By constraining tau functions of bilinear equations in the KP hierarchy, we obtain general 2N-line solitons and N-breather solutions with a periodic wave background. What needs to be emphasized are the two-soliton can be divided into non-degenerate and degenerate soliton according to the asymptotic analysis. Meanwhile, one- and two-breather solutions in a periodic wave and constant background are investigated.