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Abstract We characterize initial value problems for the defocusing Manakov system (coupled two-component nonlinear Schrödinger equation) with nonzero background and well-defined spatial parity symmetry (i.e., when each of the components of the solution is either even or odd), corresponding to boundary value problems on the half line with Dirichlet or Neumann boundary conditions at the origin. We identify the symmetries of the eigenfunctions arising from the spatial parity of the solution, and we determine the corresponding symmetries of the scattering data (reflection coefficients, discrete spectrum and norming constants). All parity induced symmetries are found to be more complicated than in the scalar (i.e., one-component) case. In particular, we show that the discrete eigenvalues giving rise to dark solitons arise in symmetric quartets, and those giving rise to dark–bright solitons in symmetric octets. We also characterize the differences between the purely even or purely odd case (in which both components are either even or odd functions of x ) and the ‘mixed parity’ cases (in which one component is even while the other is odd). Finally, we show how, in each case, the spatial symmetry yields a constraint on the possible existence of self-symmetric eigenvalues, corresponding to stationary solitons, and we study the resulting behavior of solutions.
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UV origin of discrete symmetries
We discuss the possible UV origin of discrete symmetries. We review the (i) interpretation of discrete R symmetries as discrete remnants of the Lorentz group; (ii) additional discrete transformations arising in orbifold compactifications, some of which have only been found recently; (iii) the stringy/gauge origin of family symmetries; (iv) CP violation from strings. These notes are based on an invited talk by the author at FHEP 2019 in Hyderabad.
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- Award ID(s):
- 1915005
- PAR ID:
- 10253357
- Date Published:
- Journal Name:
- Springer Proceedings in Physics book series (SPPHY, volume 248)
- Volume:
- 248
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-981-15-6292-1_62
