Space-shifted toroidal, spherical solitons and collisions for the nonlocal coupled nonlinear Schrödinger equations

Some space-shifted bright soliton solutions in terms of determinants for the space-shifted nonlocal coupled nonlinear Schrodinger (NCNLS) equations are constructed by using the improving Hirota's bilinear method. A few of 1-bright and 2-bright solitons of the NCNLS equations are derived with a function e2i gamma t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e<^>{2i\gamma t}$$\end{document} and the space-shifted term x0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_0$$\end{document}. The influence of the space-shifted parameters for the solution is significant, and some novel dynamic behaviors of the space-shifted solutions are presented. The two-bright solitons admit some novel patterns, whose amplitudes increase or decrease with time. The bright-breather soliton solutions are derived through a long wave limit of the obtained bright soliton solutions, and their collision dynamics are also investigated. And some bright solitons can occur elastic collisions, which shows that some expressions of the soliton amplitudes are independent on the phase shift factor x0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_0$$\end{document}. Some novel toroidal and spherical bright solitons, breather solitons are derived by the toroidal and spherical coordinate transformations.