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

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.