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In this paper, we characterized resonant interaction of weakly nonlinearhyperbolic waves in gas dynamics with a real gas background. An asymptoticapproach is used to study the interaction between waves, governed by the Eulerequations of gas dynamics, supplemented by a van der Waal equation of state;the evolution equation is an integro-differential equation composed of aBurgers type nonlinear term and a convolution term with a known kernel. A oneparameter family of traveling wave solutions for various values of van derWaals parameter is studied analytically and numerically. Effect of theinfluence of van der Waals parameter on the properties of traveling wavessolution is investigated. Numerical experiments on the evolution of arbitraryinitial data are performed using fractional step algorithm, describing thebehavior of convolution term in the integrodiffrential equation. The existenceof non breaking for all time solutions is substantiated numerically.

Analytical and numerical study of weakly nonlinear hyperbolic waves in a van der Waals gas