KC7016 - Linear & Non Linear Waves

What will I learn on this module?

Wave phenomena appear everywhere in nature, from water waves to magnetic materials, from optics to weather forecasts, hence their description and understanding is of fundamental importance both from the theoretical and the applicative point of view.
You will learn the mathematical theory of wave motion including both linear and nonlinear behaviour. Applications include the understanding of shock waves and coherent structures, such as solitons, of some famous integrable partial differential equations that arise from standard modelling processes.

The syllabus includes topics from

Linear wave equations
Wave propagation; characteristics; dispersion relations; group velocity; wave energy; applications.

Nonlinear wave equations
Dispersive and hyperbolic waves; stationary waves; transport and travelling waves; dissipation and shock structures; Burger's equation; applications.

Nonlinear integrable waves equations
e.g. Korteweg-de Vries (KdV) equation; solitons; Inverse Spectral Transform (IST) for the KdV; examples of nonlinear integrable waves and their applications; multiscale expansion and integrability of dispersive wave equations.

How will I learn on this module?

You will learn through a series of lectures and problem-solving workshops which include classroom discussions and presentations. Workshop will be scheduled at regular intervals to allow exploration of the theoretical background to the techniques covered in the lectures as well as attempt the practical analysis of selected problems. Lectures allow you to witness the development of the relevant theoretical aspects behind non linear wave phenomena and understand how to apply the techniques and interpret the results through many examples.

Formative feedback is available in the classes as you get to grips with new techniques and solve problems. In addition, we operate an open door policy where you can meet with your module tutor to seek further advice or help if required. Your ability to use the relevant theory to identify and evaluate solutions to set problems is assessed in a closed-book exam at the end of the module.

General feedback on the exam will be given in a specially-arranged feedback session in semester 2 and individual feedback will be written on scripts. An opportunity to discuss work further will be available on an individual basis when work is returned and also through the open door policy.

How will I be supported academically on this module?

Direct contact with the module team during the lectures and workshops will involve participation in both general class discussions as well as one to one discussions during the problem-solving workshops. This gives you a chance to get immediate feedback pertinent to your particular needs in this session. Further feedback and discussion with the module team are also available at any time through our open door policy. In addition, all teaching materials, selected computer programmes and supplementary material (such as relevant research articles) are available through the e-learning portal.

What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk
(Reading List service online guide for academic staff this containing contact details for the Reading List team – http://library.northumbria.ac.uk/readinglists)

What will I be expected to achieve?

Knowledge & Understanding:
1. Analyse one dimensional nonlinear wave equations in terms of simple waves and discontinuities (KU1, KU2, KU3).
2. Solve selected one dimensional nonlinear wave propagation problems (KU1, KU2, KU3).

Intellectual / Professional skills & abilities:
3. Develop efficient solutions for advanced problems in nonlinear wave theory (IPSA1, IPSA2).

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
4. Manage your own learning, through knowledge of available reading sources, including advanced texts and research papers (PVA1, PVA3).
5. Effectively and concisely communicate complex astrophysics-based ideas in written form (PVA1, PVA3).

How will I be assessed?

Examination (100%) – 1, 2, 3, 4, 5

FORMATIVE – 1, 2, 3, 4, 5
Formative assessment will be available during problem-solving workshops through normal lecturer-student interactions and discussions around the set questions, allowing students to extend, consolidate and evaluate their knowledge.

Formative feedback will be provided on student work and errors in understanding will be addressed reactively using individual discussion. Solutions to problems will be provided after the students have attempted the questions, allowing students to receive feedback on the correctness of their solutions and to seek help if matters are still not clear.


Complex Analysis



Module abstract

‘Linear and Non-linear Waves’ is designed to introduce you to the theory of wave motion including both linear and nonlinear behaviour. Applications include the understanding of shock waves and coherent structures, such as solitons, of some famous integrable partial differential equations that arise from standard modelling processes.

You will learn through a combination of lectures and problem-solving/computer-based workshops. Lectures give a formal introduction to theoretical aspects while the workshops offer the opportunity to deepen the knowledge by applying the theory to problems coming from physics, biology, chemistry and engineering. Workshops will be an opportunity to address open research problems; they will often address topics with links beyond the discipline, thus also strengthening your transferable skills and employability.

The module is assessed with a formal closed-book computer-laboratory-based examination, which will cover all aspects of the module and will assess your problem solving abilities when applied to new and unseen problems.

Course info

UCAS Code G101

Credits 20

Level of Study Undergraduate

Mode of Study 4 years full-time or 5 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2022 or September 2023

Fee Information

Module Information

All information on this course page is accurate at the time of viewing.

Our Campus based courses starting in 2022 and 2023 will be delivered on-campus with supporting online learning content. We continue to monitor government and local authority guidance in relation to Covid-19 and we are ready and able to adjust the delivery of our education accordingly to ensure the health and safety of our students and staff.

On-campus contact time is subject to increase or decrease in line with any additional restrictions, which may be imposed by the Government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors. This could potentially mean increased or fully online delivery, should such restrictions on in-person contact time be required.


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