Dynamic behaviors of general N-solitons for the nonlocal generalized nonlinear Schrödinger equation

The general N-solitons of nonlocal generalized nonlinear Schrödinger equations with third-order, fourth-order and fifth-order dispersion terms and nonlinear terms (NGNLS) are studied. Firstly, the Riemann–Hilbert problem and the general N-soliton solutions of NGNLS equations were given. Then, we study the symmetry relations of the eigenvalues and eigenvectors related to the scattering data which involve the reverse-space, reverse-time and reverse-space-time reductions. Thirdly, some novel solitons and the dynamic behaviors which corresponded to novel eigenvalue configurations and the coefficients of higher-order terms are given. In all the three NGNLS equations, their solutions often collapse periodically, but can remain bounded or nonsingular for wide ranges of soliton parameters as well. In addition, it is found that the higher-order terms of the NGNLS equations not only affect the amplitude variation of the soliton, but also influence the singularity and the motion of the soliton.