| The article focuses on the(2+1)dimensional Hirota-Maccari equation and(2+1)dimensional nonlocal Fokas equation.By using the Hirota bilinear method and the KP reduction method,we get exact solutions of the Hirota-Maccari equation and the nonlocal Fokas equation,and analyze their dynamic behavior with corresponding mathematical tools.At the same time,the modulation instability of the equation is also studied.The article is mainly divided into the following parts:In the first chapter,we mainly introduce the soliton theory,KP reduction method and the research overview of the exact solutions simply.In the second chapter,the bilinear method of the Hirota-Maccari equation and the tau function form of the semi-rational solutions are constructed.We first explored the special circumstances of semi-rational solutions-rational solutions,and found the bright lump,bi-model lump,dark lump solutions.At the same time,we also use modulation instability to explain the existence of rogue waves.For semi-rational solutions and high-level semi-rational solutions,the multiple split and annihilation phenomenon between lumps and line solitons are discussed.In the third chapter,the rational solutions and semi-rational solutions to the nonlocal Fokas equation are studied.Due to the existence of nonlocal conditions,the tau function is constructed by the KP reduction method requires additional parameter constraints.In this case,the rational and semi-rational solutions are even-order tau function solutions which are different from local cases.By using maple and other tools,five types of line soliton solutions,the double lump solutions,the mixed forms of lumps and line solitons are given and the dynamic behavior analysis is carried out simply. |
