Dynamics of lump–soliton solutions to the [formula omitted]-symmetric nonlocal Fokas system

Abstract

We use the bilinear Kadomtsev–Petviashvili (KP) hierarchy reduction method for deriving new families of explicit lump–soliton solutions to the PT-symmetric nonlocal Fokas system. These lump–soliton solutions are semi-rational solitons that are classified into three different species under appropriate parametric restrictions: line solitons, rational lumps, and semi-rational lump–soliton solutions. There are three different fundamental lump–soliton solutions: two-line soliton, rational two-lump solution, and two-lump–two-line-soliton solution. The two-line-soliton solution displays five patterns according to their asymptotic analysis, the rational two-lump solution possesses six distinct patterns, and the two-lump–two-line-soliton solution has four different patterns. The two-lump–two-line-soliton solution displays inelastic interaction phenomena consisting of two lumps fusing into or fissioning from the two-line soliton. The multi-lump-soliton solutions illustrate the superimposition of N (N≥2) individual fundamental lump–soliton solutions: 2N-line solitons, rational 2N-lumps, and 2N-lump–2N˜-line solitons (N˜≤N). The higher-order lump–line-soliton solutions consist of rational 2n0-lump (n0≥2) solutions or 2n0-lump–two-line-soliton solutions.