Complex PT-invariant cnoidal and hyperbolic solutions of several real nonlinear equations

Abstract

For a large number of real nonlinear equations, either continuous or discrete, uncoupled or coupled, we show that whenever these equations admit real cnoidal wave solutions, they also admit complex PT-invariant cnoidal (and hyperbolic) wave solutions. Further, we show that for real coupled field theories, one cannot only have complex PT-invariant cnoidal wave solutions with PT eigenvalue +1 or −1 in both the fields but one can also have ‘mixed’ cnoidal wave solutions with PT eigenvalue +1 in one field and −1 in the other field. In the appropriate limit the corresponding hyperbolic solutions are obtained.