caa a22 4500 46910886X CHVBK 20180323133104.0 cr unu---uuuuu 170328e19921201xx s 000 0 eng 10.1007/BF00424364 doi (NATIONALLICENCE)springer-10.1007/BF00424364 The (3+1)-dimensional Monge-Ampère equation in discontinuity wave theory: Application of a reciprocal transformation [Elektronische Daten] [Andrea Donato, Usha Ramgulam, Colin Rogers] It is shown that the complete exceptionality condition for discontinuity waves associated with a second-order non-linear hyperbolic equation of the form $$u_u + f(x_i ,{\text{ }}t,{\text{ }}u,{\text{ }}u_i {\text{ }}u_u ,{\text{ }}u_{jk} ) = 0,{\text{ }}i = 1,{\text{ 2, 3; }}j \leqslant k$$ leads to a Monge-Ampère-type equation in 3+1 dimensions. Application of a novel reciprocal transformation shows that an important subclass may be reduced to linear canonical form. Specialization to 1+1 dimensions yields linearization of a Boillat-type equation satisfying the complete exceptionality criterion. In this last case the transformation allowing the linearization coincide with the one introduced by Hoskins and Bretherton in the theory of atmospheric frontogenesis and so-called geostrophic transformation. Finally, always in 1+1 dimensions, we show that the Monge-Ampère equation is also strictly exceptional, i.e. the only possible shocks are characteristic. Kluwer Academic Publishers, 1992 Discontinuity nationallicence Waves Reciprocal transformation nationallicence Exceptionality nationallicence Donato Andrea Dipartimento di Matematica, Facolta' di Scienze, Universita di Messina, 98166 S., Agata, Italy aut Ramgulam Usha Department of Mathematical Sciences, Loughborough University of Technology, UK aut Rogers Colin Department of Mathematical Sciences, Loughborough University of Technology, UK aut Meccanica Kluwer Academic Publishers 27/4(1992-12-01), 257-262 0025-6455 27:4<257 1992 27 11012 https://doi.org/10.1007/BF00424364 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00424364 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Donato Andrea Dipartimento di Matematica, Facolta' di Scienze, Universita di Messina, 98166 S., Agata, Italy aut NATIONALLICENCE 700 1- Ramgulam Usha Department of Mathematical Sciences, Loughborough University of Technology, UK aut NATIONALLICENCE 700 1- Rogers Colin Department of Mathematical Sciences, Loughborough University of Technology, UK aut NATIONALLICENCE 773 0- Meccanica Kluwer Academic Publishers 27/4(1992-12-01), 257-262 0025-6455 27:4<257 1992 27 11012 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer