Integrable nonlinear Klein-Gordon systems with \(\mathcal{PT}\) nonlocality and/or space-time exchange nonlocality. (English) Zbl 1495.81060
Summary: In additional to the parity \(( \mathcal{P})\) symmetric, time reversal \((\mathcal{T})\) symmetric, and \(\mathcal{PT}\) symmetric nonlocal integrable systems, some other types of nonlocal integrable Klein-Gordon models with the space-time exchange nonlocality and the moving nonlocality are proposed. The Lax pairs of the established nonlinear nonlocal Klein-Gordon equations are explicitly given. A special soliton solution, composed of \(\mathcal{PT} \)-symmetric part and \(\mathcal{PT} \)-antisymmetric part, is illustrated with the shape change.
MSC:
| 81Q80 | Special quantum systems, such as solvable systems |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 18D65 | Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads) |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C08 | Soliton solutions |
Keywords:
nonlocal integrable Klein-Gordon models; \(\mathcal{PT}\) symmetry; space-time exchange symmetry; moving nonlocalityReferences:
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