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

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

2008-01-21

arxiv.org/abs/0801.3292v1

J.Math.Phys.49:043502,2008

Physics

Mathematical Physics

30 pages

Scientific paper

10.1063/1.2898094

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.

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