# Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs

Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs A reduction procedure for determining double-wave exact solutions to first-order hyperbolic systems of PDEs is proposed. The basic idea is to reduce the integration of the governing hyperbolic set of N partial differential equations to that of a $$2 \times 2$$ 2 × 2 reduced hyperbolic model along with a further differential constraint. Therefore, the method of differential constraints is used in order to solve the auxiliary $$2 \times 2$$ 2 × 2 system. An example of interest to viscoelasticity is presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

# Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs

, Volume 68 (5) – Aug 19, 2017
16 pages

/lp/springer_journal/double-wave-solutions-to-quasilinear-hyperbolic-systems-of-first-order-p8f1ez6plr
Publisher
Springer Journals
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-017-0850-4
Publisher site
See Article on Publisher Site

### Abstract

A reduction procedure for determining double-wave exact solutions to first-order hyperbolic systems of PDEs is proposed. The basic idea is to reduce the integration of the governing hyperbolic set of N partial differential equations to that of a $$2 \times 2$$ 2 × 2 reduced hyperbolic model along with a further differential constraint. Therefore, the method of differential constraints is used in order to solve the auxiliary $$2 \times 2$$ 2 × 2 system. An example of interest to viscoelasticity is presented.

### Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: Aug 19, 2017

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations