PT-symmetry breaking in complex nonlinear wave equations and their deformations

Cavaglia, A., Fring, A. & Bagchi, B. (2011). PT-symmetry breaking in complex nonlinear wave equations and their deformations. Journal of Physics A: Mathematical and Theoretical, 44(32), p. 325201. doi: 10.1088/1751-8113/44/32/325201

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We investigate complex versions of the Korteweg–deVries equations and an Ito-type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic and elliptic solutions for these models including those which are physically feasible in an obvious sense, that is those with real energies, but also those with complex energy spectra. The reality of the energy is usually attributed to different realizations of an antilinear symmetry, as for instance -symmetry. It is shown that the symmetry can be spontaneously broken in two alternative ways either by specific choices of the domain or by manipulating the parameters in the solutions of the model, thus leading to complex energies. Surprisingly, the reality of the energies can be regained in some cases by a further breaking of the symmetry on the level of the Hamiltonian. In many examples, some of the fixed points in the complex solution for the field undergo a Hopf bifurcation in the -symmetry breaking process. By employing several different variants of the symmetries we propose many classes of new invariant extensions of these models and study their properties. The reduction of some of these models yields complex quantum mechanical models previously studied.

Item Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science

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