**Author/Developer:**
Jonathan A. Sherratt,
Department of Mathematics and
Maxwell Institute for Mathematical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK.

**Summary:**
WAVETRAIN is a free, open-source
software package for investigating periodic
travelling wave solutions of partial differential equations.
Typically such equations will contain a number of parameters.
WAVETRAIN requires that one of these
be selected; this parameter is referred to as the control
parameter. Focussing on periodic
travelling waves introduces an additional parameter, the wave speed.
The basic task performed by
WAVETRAIN is the calculation of the region of the control
parameter - wave speed
plane in which periodic travelling waves exist, and additionally
where they are stable. WAVETRAIN's calculations all use the method of
numerical continuation.
WAVETRAIN is intended to be easy to use, even for users with limited
mathematical/computational background. In particular, the
input files for WAVETRAIN are all simple text files: users are not
required to write any computer programs, and do not need expertise in
any programming language or other software.
WAVETRAIN includes a plotter to visualise the
results of its calculations. WAVETRAIN plots are
publication-quality, and
can be fine-tuned by the user if required.
WAVETRAIN also provides detailed output data files that
are accessible to the user if required, and that have an
easily comprehensible format.

**Funding:** WAVETRAIN has been supported by the
Leverhulme Trust
(Research Fellowship to JAS).

**System Requirements:**
The main requirement of WAVETRAIN is a unix-like operating system.
Users with a Windows operating system can use
WAVETRAIN via a virtual machine, for which there is freely
available software. The WAVETRAIN user guide gives a full description
of the user requirements.

**Use of other software:**
WAVETRAIN makes use of the software packages
AUTO,
BLAS,
EISPACK,
LAPACK
and
MINPACK.
The relevant routines from these packages are distributed, with
permission, as part of WAVETRAIN.

**Copyright/distribution/disclaimer:** please read the statement
here.
Please note that redistribution of either WAVETRAIN or the WAVETRAIN
user guide are prohibited.

**Downloading:** instructions for downloading and installing
WAVETRAIN are given
here.

**References:**
If you publish research done using WAVETRAIN, please cite

- J.A. Sherratt: Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations. Applied Mathematics & Computation 218, 4684-4694 (2012). DOI:10.1016/j.amc.2011.11.005

If your research includes results on wave stability, please also cite

- J.D.M. Rademacher, B. Sandstede, A. Scheel: Computing absolute and essential spectra using continuation. Physica D 229, 166-183 (2007). DOI:10.1016/j.physd.2007.03.016

- J.A. Sherratt: Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations. Advances in Computational Mathematics 39, 175-192 (2013). DOI:10.1007/s10444-012-9273-0

**Feedback:** comments on WAVETRAIN, whether positive or negative,
are strongly encouraged. The e-mail address for all feedback is
j.a.sherratt@hw.ac.uk
(please include
the word wavetrain, in upper or lower case, in the subject heading of
your message).

**Release history:**

WAVETRAIN0.0 was released on 13 September 2011.

WAVETRAIN0.1 was released on 25 September 2011.
*This slightly amended version was released in response to a request
from a potential user for the inclusion of a
built-in step function in the*
`equations.input`

*file.*

WAVETRAIN1.0 was released on 15 August 2013.
*This release has a number of significant improvements and
extensions. These include a new command to calculate the loci of folds of
the periodic travelling wave solution branch, a complete overhaul of
the processing within the plotter, and a new plotting command to
shade specified regions of the control parameter -- wave speed plane.*

WAVETRAIN1.1 was released on 7 November 2013.
*This slightly amended version corrects various minor bugs.*

WAVETRAIN1.2 was released on 23 April 2015.
*This version has various minor improvements to both running and
plotting commands, including some improvement in computational
efficiency.*

A complete list of changes between different versions of the software is given here.

All old releases of WAVETRAIN can be downloaded from the WAVETRAIN archive.