Solvable cubic resonant systems. (English) Zbl 1429.83009
The authors have found a new conserved quantity for a class of nonlinear partial differential system of equations which provides resonant and periodic properties. The authors give a rigorous proof of this statement. Analogies can be found in applications of the Gross-Pitaevsky equation and nonlinear wave equations in an Anti-de Sitter spacetime. For further connections with physics, the reviewer recommends the book: [J. Liu et al., Nonlinear adiabatic evolution of quantum systems. Geometric phase and virtual magnetic monopole. Singapore: Springer (2018; Zbl 1405.81009)].
Reviewer: Alex B. Gaina (Chisinau)
MSC:
| 83C15 | Exact solutions to problems in general relativity and gravitational theory |
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 35L65 | Hyperbolic conservation laws |
| 35B34 | Resonance in context of PDEs |
| 35G20 | Nonlinear higher-order PDEs |
| 35L05 | Wave equation |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
Keywords:
partial differential equations; resonances; analytic solutions; periodicity; Gross-Pitaevsky equation; anti-de Sitter spacetime; conserved quantitiesCitations:
Zbl 1405.81009References:
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