Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems
We aim to discuss about how to construct and classify nonlocal PT-symmetric integrable equations via nonlocal group reductions of matrix spectral problems. The nonlocalities considered are reverse-space, reverse-time and reverse-spacetime, each of which can involve either the transpose or the Hermit...
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Elsevier
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/1fe9b55b5c294e539dc28d9c7da6659e |
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| Sumario: | We aim to discuss about how to construct and classify nonlocal PT-symmetric integrable equations via nonlocal group reductions of matrix spectral problems. The nonlocalities considered are reverse-space, reverse-time and reverse-spacetime, each of which can involve either the transpose or the Hermitian transpose. The associated spectral problems are used to formulate a kind of Riemann–Hilbert problems and thus inverse scattering transforms. Soliton solutions are generated from specific Riemann–Hilbert problems with the identity jump matrix. We focus on two expository examples: nonlocal PT-symmetric matrix nonlinear Schrödinger and modified Korteweg–de Vries equations. |
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