Fronts in inhomogeneous wave equations
Lead Research Organisation:
University of Surrey
Department Name: Registry
Abstract
This project considers the existence and stability of fronts in a wave equation with an inhomogeneity. There are two possible directions for the project. One is the study of the interaction of the inhomogeneity with travelling fronts. Numerically the existence of travelling periodic patterns at either side of the discontinuity is observed. This project could focus on understanding the underlying mechanisms for these patterns. Another area for an extension is the study of fronts in coupled inhomogeneous wave equations.
Organisations
People |
ORCID iD |
| Jacob Brooks (Student) |
Publications
Brooks J
(2019)
Existence of stationary fronts in a system of two coupled wave equations with spatial inhomogeneity
in Nonlinearity
Brooks Jacob
(2021)
Inhomogeneous semi-linear wave equations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509772/1 | 30/09/2016 | 29/09/2021 | |||
| 1802706 | Studentship | EP/N509772/1 | 30/09/2016 | 30/03/2020 | Jacob Brooks |
| Description | We have investigated the existence of stationary wave solutions in a wave equation with spatial defect. The equation investigated has applications to physics and biology. Using the known stationary waves we show that in certain circumstances they can alter their shape and become 'new' waves. Currently we are developing the mathematics to describe the interaction of travelling waves with spatial defects. |
| Exploitation Route | Research in wave equations with spatial defects is very active. Our results provide an increased understanding in this area of mathematics and physics. |
| Sectors | Education Other |
| URL | https://iopscience.iop.org/article/10.1088/1361-6544/ab2ca5 |