A class of quasilinear hyperbolic reducible systems, which involve two first order homogeneous equations in one space dimensions and time, is characterized by requiring the associated hodograph system to reduce to a particular canonical form allowing explicit integration. Furthermore for the mathematical models so determined, it is shown that any two pulses travelling in opposite directions interact on colliding but emerge with unaffected profiles from the interaction region. Such a kind of situation, though in a different physical context, is similar to that occurring in nonlinear dispersive media when two solitons collide but emerge unaltered from the interaction. Finally the governed sytem of isentropic fluid-dynamics is considered. In this case it is determined a set of multiparameter pressure-density laws which allow for the soliton-like interactions studied herein.
ON A CLASS OF QUASILINEAR HYPERBOLIC REDUCIBLE SYSTEMS ALLOWING FOR SPECIAL WAVE INTERACTIONS
CURRO', Carmela;FUSCO, Domenico
1987-01-01
Abstract
A class of quasilinear hyperbolic reducible systems, which involve two first order homogeneous equations in one space dimensions and time, is characterized by requiring the associated hodograph system to reduce to a particular canonical form allowing explicit integration. Furthermore for the mathematical models so determined, it is shown that any two pulses travelling in opposite directions interact on colliding but emerge with unaffected profiles from the interaction region. Such a kind of situation, though in a different physical context, is similar to that occurring in nonlinear dispersive media when two solitons collide but emerge unaltered from the interaction. Finally the governed sytem of isentropic fluid-dynamics is considered. In this case it is determined a set of multiparameter pressure-density laws which allow for the soliton-like interactions studied herein.Pubblicazioni consigliate
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