General soliton, line breather and (semi-)rational solutions for the nonlocal long-wave-short-wave resonance interaction equation

In this work, the general solutions of the nonlocal long-wave-short-wave resonance interaction (LSRI) equation with nonzero boundary conditions are investigated by using the Hirota's bilinear method and Kadomtsev-Petviashvili hierarchy reduction method. We discussed the cases where N is odd and even, which have a significant impact on the background wave. When N is odd, the solutions are located in the periodic background, while it is on the constant background when N is even. Different forms of solutions are discussed in detail, including the general soliton, line breather and (semi-)rational solutions. For these solutions of the nonlocal LSRI equation, we have obtained a variety of rich and interesting images are obtained through theoretical and graphical analysis, and most of them cannot correspond to the local equation.