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Integrable (3 + 1)-Dimensional Generalization for the Dispersionless Davey–Stewartson System

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Abstract

This paper introduces a (3 + 1)-dimensional dispersionless integrable system, utilizing a Lax pair involving contact vector fields, in alignment with methodologies presented by Sergyeyev in 2014. 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.

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Acknowledgements

The author thanks the financial support from the University of Cádiz through the internal funding program ‘Plan Propio de Estímulo y Apoyo a la Investigación y Transferencia 2022/2023’, and from Junta de Andalucía through the research group FQM–377. Special thanks are extended to A. Sergyeyev for stimulating discussions and encouragement. The author would also like to express gratitude to the anonymous referees for their insightful comments and suggestions, which have significantly contributed to the improvement of this work.

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  1. Departamento de Matemáticas, Universidad de Cádiz - UCA, Polígono Río San Pedro, 11510, Puerto Real, Cádiz, Spain

    Antonio J. Pan-Collantes

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AJPC wrote the main manuscript text and perform al the revisions.

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Pan-Collantes, A.J. Integrable (3 + 1)-Dimensional Generalization for the Dispersionless Davey–Stewartson System. Qual. Theory Dyn. Syst. 23, 151 (2024). https://doi.org/10.1007/s12346-024-01009-9

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