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

Journal of Physics A: Mathematical and Theoretical

Volumn 44, Issue 32, 2011, Pages

  Cavaglia, Andrea ^a   Fring, Andreas ^a   Bagchi, Bijan ^b  

^a CITY UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF CALCUTTA   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80051481032     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/44/32/325201     Document Type: Article

References (43)

1. Heisenberg W 1943 Die beobachtbaren Gren in der Theorie der Elementarteilchen Zeit. fr Phys. 120 513-38
2. Eden R J, Landshoff P V, Olive D I and Polkinghorne J C 1966 The Analytic S-matrix (Cambridge: Cambridge University Press)
3. Rotter I 2009 A non-Hermitian Hamilton operator and the physics of open quantum systems J. Phys. A: Math. Theor. 42 153001
4. Bender C M and Boettcher S 1998 Real spectra in non-Hermitian Hamiltonians having PT symmetry Phys. Rev. Lett. 80 5243-6 (Pubitemid 128626511)
5. Bender C M 2007 Making sense of non-Hermitian Hamiltonians Rep. Prog. Phys. 70 947-1018
6. Mostafazadeh A 2010 Pseudo Hermitian representation of quantum mechanics Int. J. Geom. Meth. Mod. Phys. 7 1191-306
7. Assis P 2010 Non-Hermitian Hamiltonians in Field Theory (Saarbrcken: VDM)
8. Rter C E, Makris R, El-Ganainy K G, Christodoulides D N, Segev M and Kip D 2010 Observation of parity-time symmetry in optics Nat. Phys. 6 192-5
9. Fagotti M, Bonati C, Logoteta D, Marconcini P and Macucci M 2011 Armchair graphene nanoribbons: PT-symmetry breaking and exceptional points without dissipation arXiv:1102.2129v1 [cond-mat.mes-hall]
10. Nanayakkara A 2004 Classical trajectories of 1D complex non-Hermitian Hamiltonian systems J. Phys. A: Math. Gen. 37 4321-34 (Pubitemid 38554272)
11. Bender C M, Holm D D and Hook D W 2007 Complex trajectories of a simple pendulum J. Phys. A: Math. Theor. 40 F81-9
12. Bender C M, Brody D C and Hook D W 2008 Quantum effects in classical systems having complex energy J. Phys. A: Math. Theor. 41 352003
13. Bender C M, Hook D W and Kooner K S 2010 Classical particle in a complex elliptic potential J. Phys. A: Math. Theor. 43 165201
14. Bender C M, Holm D D and Hook D W 2007 Complexified dynamical systems J. Phys. A: Math. Theor. 40 F793-804
15. Bender C M, Feinberg J, Hook D W and Weir D J 2009 Chaotic systems in complex phase space Pramana J. Phys. 73 453-70
16. Fring A 2006 A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models Mod. Phys. Lett. 21 691-9 (Pubitemid 43396758)
17. Fring A and Znojil M 2008 -Symmetric deformations of Calogero models J. Phys. A: Math. Theor. 41 194010
18. Assis P E G and Fring A 2009 From real fields to complex Calogero particles J. Phys. A: Math. Theor. 42 425206
19. Fring A and Smith M 2010 Antilinear deformations of Coxeter groups, an application to Calogero models J. Phys. A: Math. Theor. 43 325201
20. Bender C M and Hook D W 2010 Tunneling in classical mechanics arXiv:1011.0121
21. Bender C M and Arpornthip T 2009 Conduction bands in classical periodic potentials Pramana J. Phys. 73 259-68
22. Bender C M, Hook D W, Meisinger P N and Wang Q-h 2010 Complex correspondence principle Phys. Rev. Lett. 104 061601
23. Bender C M, Brody D C, Chen J and Furlan E 2007 -symmetric extension of the Korteweg-de Vries equation J. Phys. A: Math. Theor. 40 F153-60
24. Fring A 2007 -Symmetric deformations of the Korteweg-de Vries equation J. Phys. A: Math. Theor. 40 4215-24
25. Bagchi B and Fring A 2008 -symmetric extensions of the supersymmetric Korteweg-de Vries equation J. Phys. A: Math. Theor. 41 392004
26. Bender C M and Feinberg J 2008 Does the complex deformation of the Riemann equation exhibit shocks? J. Phys. A: Math. Theor. 41 244004
27. Curtright T L and Fairlie D B 2008 Euler incognito J. Phys. A: Math. Theor. 41 244009
28. Bender C M, Cooper F, Khare A, Mihaila B and Saxena A 2009 Compactons in -symmetric generalized Korteweg-de Vries Equations Pramana J. Phys. 73 375-85
29. Assis P E G and Fring A 2010 Compactons versus Solitons Pramana J. Phys. 74 857-65
30. Wigner E 1960 Normal form of antiunitary operators J. Math. Phys. 1 409-13
31. Ergun E and Saglam M 2010 On the metric of a non-Hermitian model Rep. Math. Phys. 65 367-78
32. Fuchssteiner B 1982 The Lie algebra structure of degenerate Hamiltonian and bi-Hamiltonian systems Prog. Theor. Phys. 68 1082-104
33. Oevel W 1983 On the integrability of the Hirota-Satsuma system Phys. Lett. A 94 404-7
34. Yang L, Yang K and Luo H 2000 Complex version KdV equation and the periods solution Phys. Lett. A 267 331-4
35. Fushchych W I, Serov N I and Ahmerov T K 1991 On the conditional symmetry of the generalized KdV equation Rep. Ukr. Acad. Sci. 12 28
36. Arrowsmith D K and Place C 1992 Dynamical Systems (London: Chapman and Hall)
37. Bagchi B, Das S and Ganguly A 2010 New exact solutions of a generalized shallow water wave equation Phys. Scr. 82 025003
38. Hirota R and Satsuma J 1981 Soliton solutions of a coupled Korteweg-de Vries equation Phys. Lett. A 85 407-8
39. Satsuma J and Hirota R 1982 A coupled KdV equation is one case of the four-reduction of the KP Hierachy J. Phys. Soc. Japan 51 3390-7
40. Ito M 1982 Symmetries and conservation laws of a coupled nonlinear wave equation Phys. Lett. A 91 335-8
41. Kawamoto S 1984 Cusp soliton solutions of the Ito-type coupled nonlinear wave equation J. Phys. Soc. Japan 53 1203-5
42. Guha-Roy C, Bagchi B and Sinha D 1986 Traveling-wave solutions and the coupled Korteweg-de Vries equation J. Math. Phys. 27 2558-61
43. Anderson A G, Bender C M and Morone U I 2011 Periodic orbits for classical particles having complex energy arXiv:1102.4822