Propagation and Interaction of Nonlinear Waves to Quasilinear Equations

Danilov, V. G.; Shelkovich, V. M.

doi:10.1007/978-3-0348-8370-2_28

V. G. Danilov¹⁰ &
V. M. Shelkovich¹¹

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 140))

537 Accesses
2 Citations

Abstract

A method for analytical description of nonlinear wave interaction is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 84.99; Price excludes VAT (USA)

Softcover Book: USD 109.99; Price excludes VAT (USA)

Hardcover Book: USD 109.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

V. M. ShelkovichAn associative-commutative algebra of distributions that includes multiplicators generalized solutions of nonlinear equationsMathematical Notices, 57 (1995), No. 5, 765–783.
MathSciNet MATH Google Scholar
V. G. Danilov, V. P. Maslov, V. M. ShelkovichAlgebra of singularities of singular solutions to first-order quasilinear strictly hyperbolic systemsTheor. Math. Phys., 114 (1998), No. 1, 1–42.
MathSciNet MATH Google Scholar
V. P. Maslov and V. A. TsupinNecessary conditions for the existence of infinitely narrow solitons in gas dynamicsDokl. Akad. Nauk SSSR, 246 (1979), 298–300; Engl. transl. in Soviet Phys. Dokl., 24 (1979), No. 5, 354–356.
Google Scholar
V. P. Maslov and G. A. Omel’yanov Asymptotic soliton-form solutions of equations with small dispersionUspekhi Mat. Nauk, 36 (1981), No. 3, 63–126, Engl. transi. in Russian Math. Surveys, 36 (1981), No. 3, 73–119;
MathSciNet MATH Google Scholar
F. Demengel and D. SerreNonvanishing singular parts of measure valued solutions for scalar hyperbolic equationsCommun. in Partial Diff. Eq., 16 (1991), 221–254.
MathSciNet MATH Google Scholar
D. Tan, T. Zhang, Y. ZhengDelta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation lawJ. Diff. Eq., 112 (1994), 1–32.
Article MathSciNet MATH Google Scholar
O. A. OleinikDiscontinuous solutions of nonlinear equationsUspekhi Mat. Nauk (N.S.), 1957, 12 (1957), No. 3, 3–73; Engl. transi. in Amer. Math. Soc. Transi. Ser., 2, 26, 95–172.
MathSciNet Google Scholar
V. G. Danilov and V. M. Shelkovich, Propagation of infinitely narrow 6-solitons http://www.arXiv.org/abs/math-ph/0012002

Download references

Author information

Authors and Affiliations

Moscow Technical University of Communication and Informatics, Russia
V. G. Danilov
St.-Petersburg State Architecture and Civil Engineering University, Russia
V. M. Shelkovich

Authors

V. G. Danilov
View author publications
You can also search for this author in PubMed Google Scholar
V. M. Shelkovich
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, Leipzig, 04103, Germany
Heinrich Freistühler
Otto-von-Guericke-University, Institute of Analysis and Numerical Mathematics, PSF 4120, Magdeburg, 39106, Germany
Gerald Warnecke

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Danilov, V.G., Shelkovich, V.M. (2001). Propagation and Interaction of Nonlinear Waves to Quasilinear Equations. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 140. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8370-2_28

Download citation

DOI: https://doi.org/10.1007/978-3-0348-8370-2_28
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9537-8
Online ISBN: 978-3-0348-8370-2
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics