Complex PT-symmetric extensions of the nonlinear ultra-short light pulse model

The short pulse equation u(xt) = u + 1/2 (u(2)u(x))(x) is PT symmetric, which arises in nonlinear optics for the ultra-short pulse case. We present a family of new complex PT-symmetric extensions of the short pulse equation, i[(iu(x))(sigma)](t) = au + bu(m) + ic[u(n)(iu(x))(epsilon)](x) (sigma, epsilon, a, b, c, m, n is an element of R), based on the complex PT-symmetric extension principle. Some properties of these equations with some chosen parameters are studied including the Hamiltonian structures and exact solutions such as solitary wave solutions, doubly periodic wave solutions and compacton solutions. Our results may be useful to understand complex PT-symmetric nonlinear physical models. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'.