Elliptic- and hyperbolic-function solutions of the nonlocal reverse-time and reverse-space-time nonlinear Schrodinger equations

In this paper, we obtain the stationary elliptic- and hyperbolic-function solutions of the nonlocal reverse-time and reverse-space-time nonlinear Schrodinger (NLS) equations based on their connection with the standard Weierstrass elliptic equation. The reverse-time NLS equation possesses the bounded dn$$ \mathrm{dn} $$-, cn$$ \mathrm{cn} $$-, sn$$ \mathrm{sn} $$-, sech$$ \operatorname{sech} $$-, and tanh$$ \tanh $$-function solutions. Of special interest, the tanh$$ \tanh $$-function solution can display both the dark- and antidark-soliton profiles. The reverse-space-time NLS equation admits the general Jacobian elliptic-function solutions (which are exponentially growing at one infinity or display the periodical oscillation in x$$ x $$), the bounded dn$$ \mathrm{dn} $$- and cn$$ \mathrm{cn} $$-function solutions, as well as the K$$ K $$-shifted dn$$ \mathrm{dn} $$- and sn$$ \mathrm{sn} $$ function solutions. In addition, the hyperbolic-function solutions may exhibit an exponential growth behavior at one infinity, or show the gray/bright-soliton profiles.