This article is cited in 18 papers

Uniqueness of self-similar solutions to the Riemann problem for the Hopf equation with complex nonlinearity

A. G. Kulikovskii^a, A. P. Chugainova^a, V. A. Shargatov<sup>b

a</sup> Steklov Mathematical Institute, Russian Academy of Sciences
^b National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)

Abstract: Solutions of the Riemann problem for a generalized Hopf equation are studied. The solutions are constructed using a sequence of non-overturning Riemann waves and shock waves with stable stationary and nonstationary structures.

Key words: Hopf equation, Riemann problem, KdV–Burgers equation, shock waves, Riemann waves.

UDC: 519.634

Received: 10.09.2015

DOI: 10.7868/S0044466916070115

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:7, 1355–1362

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