Donato, Andrea and Ramgulam, Usha and Rogers, Colin (2000) The(3+1)-dimensional Monge-Ampere equation in discontinuity wave theory: application of a reciprocal transformation. Memorie scientifiche di Andrea Donato. pp. 397-402.
It is shown that the completeexceptionality condition for discontinuity waves associated with a second-order non-linear hyperbolic equation of the form (..) leads to a Monge-Ampere-type equation in 3+1 dimensions.Application of a novel reciprocal trasformation shows that an important subclass may be reduced to linear canonical form.Specialization to 1+1 dimensions yields linearization of a Boillant-type equation satisfying the complete exceptionality criterior.In this last case the trasformation allowing the linearization coincide with the one introduced by Hoskinns and Bretherton in the theory of atmospheric frontogenesis and so-called geostrophic transformation.Finally,always in 1+1 dimensions,we show that the .... equation is also strictly exceptional,i.e.the only possible shocks are characteristic.
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