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Riemann problem for the Benjamin-Bona-Mahony equation

Gennady El
University of Northumbria, UK
Wednesday, May 19, 2021 - 16:00 to 17:00

I present recent analytical and numerical results on the long time dynamics of the smoothed step initial value problem or dispersive Riemann problem for the Benjamin-Bona-Mahony (BBM) equation $u_t + uu_x = u_{xxt}$.  The catalog of solutions of the dispersive Riemann problem for the BBM equation is much richer thanfor the related, integrable, Korteweg-de Vries equation and includes, along with dispersive shock waves (DSWs)and rarefaction waves, the rich variety of nonclassical dispersive hydrodynamic solutions such as dispersive Lax shocks,  expansion shocks, DSW implosion regimes and incoherent solitary wave trains.This is joint work with T. Congy, M. Hoefer and M. Shearer, arXiv:2012.14579

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