Integrable \((3 + 1)\)-dimensional generalization for the dispersionless Davey-Stewartson system. (English) Zbl 07835577
Summary: This paper introduces a \((3 + 1)\)-dimensional dispersionless integrable system, utilizing a Lax pair involving contact vector fields, in alignment with methodologies presented by A. Sergyeyev [Nonlinear Dyn. 91, No. 3, 1677–1680 (2018; Zbl 1390.37119)]. Significantly, it is shown that the proposed system serves as an integrable \((3 + 1)\)-dimensional generalization of the well-studied \((2 + 1)\)-dimensional dispersionless Davey-Stewartson system. This way, an interesting new example on integrability in higher dimensions is presented, with potential applications in analyzing three-dimensional nonlinear waves across various fields, including oceanography, fluid dynamics, plasma physics, and nonlinear optics. Importantly, the integrable nature of the system suggests that established techniques like the study of symmetries, conservation laws, and Hamiltonian structures could be applicable.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
Keywords:
three-dimensional nonlinear wave; hydrodynamic-type system; Lax pair; plasma modeling; contact vector field; conservation lawCitations:
Zbl 1390.37119References:
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