Single shock and periodic sawtooth-shaped waves in media with non-analytic nonlinearities

DOI10.1051/mmnp/2018028zbMath1407.35048OpenAlexW2803801378WikidataQ129794347 ScholiaQ129794347MaRDI QIDQ4615572

O. V. Rudenko, Claes M. Hedberg

Publication date: 29 January 2019

Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)

Full work available at URL: https://www.mmnp-journal.org/10.1051/mmnp/2018028/pdf

zbMATH Keywords

Burgers equationsexact solutionsKdV equationsKZ equationsequations of Hopfmodular solutionsOstrovsky-Vakhnenko type equationsquadratically-cubic nonlinearityshocks of rarefactiontriangular and trapezoidal saw

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Shocks and singularities for hyperbolic equations (35L67) Nonlinear effects in hydrodynamic stability (76E30) Shocks and related discontinuities in solid mechanics (74J40) Nonlinear higher-order PDEs (35G20) Hydro- and aero-acoustics (76Q05) Traveling wave solutions (35C07)

Cites Work

• Self-similar solutions of a Burgers-type equation with quadratically cubic nonlinearity
• Exact solutions of an integro-differential equation with quadratically cubic nonlinearity
• Equation admitting linearization and describing waves in dissipative media with modular, quadratic, and quadratically cubic nonlinearities
• Modular solitons
• Propagation of nonlinear acoustic waves in bimodular media with linear dissipation
• One-dimensional model of KZ-type equations for waves in the focal region of cubic and quadratically-cubic nonlinear media
• Group analysis of evolutionary integro-differential equations describing nonlinear waves: the general model
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