A M Grundland and L Lalague 1996 J. Phys. A: Math. Gen. 29 1723 doi:10.1088/0305-4470/29/8/019
Invariant and partially-invariant solutions of the equations describing a non-stationary and isentropic flow for an ideal and compressible fluid in (3 + 1) dimensions
A M Grundland and L Lalague
Show affiliationsThis paper presents a new method of constructing, certain classes of solutions of a system of partial differential equations (PDEs) describing the non-stationary and isentropic flow for an ideal compressible fluid. A generalization of the symmetry reduction method to the case of partially-invariant solutions (PISs) has been formulated. We present a new algorithm for constructing PISs and discuss in detail the necessary conditions for the existence of non-reducible PISs. All these solutions have the defect structure 
and are computed from four-dimensional symmetric subalgebras. These theoretical considerations are illustrated by several examples. Finally, some new classes of invariant solutions obtained by the symmetry reduction method are included. These solutions represent central, conical, rational, spherical, cylindrical and non-scattering double waves.
- PACS
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02.30.Jr Partial differential equations
- MSC
- Subjects
- Dates
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Issue 8 (21 April 1996)
Received 22 August 1995
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Invariant and partially-invariant solutions of the equations describing a non-stationary and isentropic flow for an ideal and compressible fluid in (3 + 1) dimensions
A M Grundland and L Lalague 1996 J. Phys. A: Math. Gen. 29 1723
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