Loughborough University is a top-ten rated university in England for research intensity (REF2014) and an outstanding 66% of the work of Loughborough’s academic staff who were eligible to be submitted to the REF was judged as ‘world-leading’ or ‘internationally excellent’, compared to a national average figure of 43%. In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career. With the support and expertise of well-respected academics, and a rich, innovative environment in which to study, postgraduate research students in the Mathematical Sciences department have one task: to further the development of mathematics and its applications through cutting-edge research. The Department tackles a wide variety of research problems, covering specialist topics across the broad spectrum of mathematics. To find out more about the research themes within the Department, and the opportunities available, click here. Quasilinear systems describe a class of nonlinear waves where dispersive effects can be neglected. Our team at Loughborough has proposed a novel approach to the study of such systems known as the method of hydrodynamic reductions [1]. In this project we will apply the method of hydrodynamic reductions to the investigation of first-order multi-component systems of hydrodynamic type in 2+1 dimensions. The ultimate goal is a complete description of integrable systems within this class. Quasilinear integrable systems are expected to have remarkable geometric/symmetry properties and are of prime importance for the classification of multidimensional dispersive integrable models. We will apply the necessary differential-geometric condition for integrability coming from the theory of double waves [2].