Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions

Abstract

In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group-theoretical methods applied to partial differential equations involving both bosonic and fermionic variables. More specifically, we compute the Lie superalgebras of both models and perform classifications of their respective subalgebras. A systematic use of the subalgebra structures allow us to construct several classes of invariant solutions, including travelling waves, centered waves and solutions involving monomials, exponentials and radicals.

arXiv comment30 pages

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Cited by in corpus (6)

• Extended symmetry analysis of isothermal no-slip drift flux model
• Invariant solutions of the supersymmetric sine-Gordon equation
• Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model
• N=2 supersymmetric extension of a hydrodynamic system in Riemann invariants
• Invariant solutions of the supersymmetric version of a two-phase fluid flow system
• Remarks on superdifferential equations