Interaction of shock waves in gas dynamics: Uniform in time asymptotics

Abstract

We construct a uniform in time asymptotics describing the interaction of two isothermal shock waves with opposite directions of motion. We show that any smooth regularization of the problem implies the realization of the stable scenario of interaction

Novel dynamical behaviors of interaction solutions of the new (3+1)-dimensional integrable fourth-order nonlinear equation

“…It has always been a significant issue that constructing the exact solutions of nonlinear partial differential equations (NLPDEs). The exact solutions play a critical role in studying various complex phenomena, which appeared in multiple research fields such as the plasma physics, nonlinear optics, gas dynamics, nancial markets, oceanography, hydrodynamics and some other related areas (Conn and Kesner 1976;Zheltukhin et al 2015;Garca-Alvarado et al 2005;Yan 2011;Slowman et al 2017). Recently, the interaction solutions among the lump waves, rouge waves and other solitary waves of NLPDEs have attracted the attention of many scholars.…”