Integrability and Lie symmetry analysis of deformed N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{N}}$$\end{document}-coupled nonlinear Schrödinger equations

A systematic investigation to derive the Lax pair and group theoretical properties of deformed N-coupled nonlinear Schrödinger equations (N-coupled NLS) is presented. Exploiting the obtained Lie point symmetries, the corresponding similarity reductions for N=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N =1$$\end{document} and N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N = 2$$\end{document} are derived separately and show that each of them passes the Painlevé property of ordinary differential equations. Exact solution of deformed coupled NLS equations is also derived wherever possible.