Simple waves for anti-van der Waals modified Chaplygin gas in 2-D magnetohydrodynamics

Abstract

Abstract This paper presents essential findings on the reducible equations introduced by Courant and Friedrichs in their seminal work, Supersonic Flow and Shock Waves. In this paper, we discuss the presence of simple waves in a 2-D magnetohydrodynamic system with an anti-van der Waals-modified Chaplygin gas. Following the approach of Hu and Sheng (characteristic decomposition of the 2 × 2 quasilinear strictly hyperbolic systems). Appl. Math. Lett. 25(3), 262–267 (2012), and (simple waves and characteristic decompositions of quasilinear hyperbolic systems in two independent variables). Math. Methods Appl. Sci. 38(8), 1494–1505 (2015) for the characteristic decomposition of a strictly hyperbolic system, we establish the existence of simple waves for a non-reducible system. This extends Courant and Friedrichs’s fundamental finding, which was initially proposed for reducible system (R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, New York, Interscience Publishers, Inc, 1948, p. 464). These results enhance our understanding of simple wave behaviour in magnetohydrodynamic systems with modified Chaplygin gas, expanding the applicability of Courant and Friedrichs’s theoretical framework.