Novel PT-invariant solutions for a large number of real nonlinear equations

For a large number of real nonlinear equations, either continuous or discrete, integrable or nonintegrable, we show that whenever a real nonlinear equation admits a solution in terms of sech x, it also admits solutions in terms of the PT-invariant combinations sechx±itanh⁡x. Further, for a number of real nonlinear equations we show that whenever a nonlinear equation admits a solution in terms sech2x, it also admits solutions in terms of the PT-invariant combinations sech2x±isechxtanh⁡x. Besides, we show that similar results are also true in the periodic case involving Jacobi elliptic functions.