Multiple dark and antidark soliton interactions in a space shifted PT symmetric nonlocal nonlinear Schrodinger equation

The multiple dark and antidark soliton solutions for a space shifted PT symmetric nonlocal nonlinear Schrodinger (SPTNNLS) equation are constructed via the Kadomtsev-Petviashvili (KP) hierarchy reduction method and Hirota's bilinear technique and are presented by 2N x 2N Gram-type determinants. Upon the asymptotic analysis of soliton interactions, these multiple dark and antidark solitons are classified into non-degenerate and degenerate types. The amplitude values and collision coordinates of two-soliton solutions are discussed theoretically and numerically. We give all dark/antidark parameter conditions of the two-soliton solutions. The four-soliton solutions exhibit the superposition of two two-soliton solutions, and the higher-order dark and antidark soliton solutions should share similar soliton properties as the four-soliton solutions.

Automated summary

Multiple dark and antidark soliton solutions for a space shifted PT symmetric nonlocal nonlinear Schrodinger equation are constructed and classified using the Kadomtsev-Petviashvili hierarchy reduction method and Hirota's bilinear technique. The amplitude values and collision coordinates of two-soliton solutions are discussed theoretically and numerically, and the parameter conditions of these solutions are given. Furthermore, the four-soliton solutions show a superposition of two two-soliton solutions, indicating that higher-order soliton solutions should have similar properties.