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Dispersionless integrable systems occur in a wide range of applications in various areas of pure and applied mathematics. In 2+1 dimensions, there exists an efficient approach to the classification of integrable systems of this kind based on the method of hydrodynamic reductions pioneered by the Loughborough group [1]. This method has lead to extensive classification results within particularly interesting classes revealing deep relations with generalised conformal geometry, theory of hypergeometric functions and modular forms [2-4].
The goal of this project is twofold:
1. Classification of dispersionless integrable systems in 2+1 dimensions with an emphasis on multi-component systems of hydrodynamic type.
2. Reconstruction of dispersive deformations of dispersionless integrable systems based on the method of dispersive deformations of hydrodynamic reductions proposed in [5-6]. This programme is expected to lead to a new class of integrable soliton PDEs with remarkable properties and potential applications.
The project will require basic knowledge of differential equations and differential geometry, as well as familiarity with symbolic computations (Mathematica/Maple).
Dispersionless integrable systems occur in a wide range of applications in various areas of pure and applied mathematics. In 2+1 dimensions, there exists an efficient approach to the classification of integrable systems of this kind based on the method of hydrodynamic reductions pioneered by the Loughborough group [1]. This method has lead to extensive classification results within particularly interesting classes revealing deep relations with generalised conformal geometry, theory of hypergeometric functions and modular forms [2-4].
The goal of this project is twofold:
1. Classification of dispersionless integrable systems in 2+1 dimensions with an emphasis on multi-component systems of hydrodynamic type.
2. Reconstruction of dispersive deformations of dispersionless integrable systems based on the method of dispersive deformations of hydrodynamic reductions proposed in [5-6]. This programme is expected to lead to a new class of integrable soliton PDEs with remarkable properties and potential applications.
The project will require basic knowledge of differential equations and differential geometry, as well as familiarity with symbolic computations (Mathematica/Maple).
Admission Requirements
3.2+
6.5+
92+
Students are expected to have an 2.1 class honours degree in mathematics.
01 Apr 2025
3 Years
Jul
Tuition fees
Domestic
4,786
International
21,500
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Dispersionless Integrable Systems In 2+1 Dimensions PhD
Loughborough University, Loughborough, United Kingdom
# 201-250QS Subject Rankings
36 monthsProgramme duration
21,500 Tuition Fee/year
01 Apr, 2025Application Deadline
Programme overview
Main Subject
Mathematics
Degree
PhD
Study Level
PHD
Study Mode
On Campus
Dispersionless Integrable Systems In 2+1 Dimensions PhD
Dispersionless integrable systems occur in a wide range of applications in various areas of pure and applied mathematics. In 2+1 dimensions, there exists an efficient approach to the classification of integrable systems of this kind based on the method of hydrodynamic reductions pioneered by the Loughborough group [1]. This method has lead to extensive classification results within particularly interesting classes revealing deep relations with generalised conformal geometry, theory of hypergeometric functions and modular forms [2-4].
The goal of this project is twofold:
1. Classification of dispersionless integrable systems in 2+1 dimensions with an emphasis on multi-component systems of hydrodynamic type.
2. Reconstruction of dispersive deformations of dispersionless integrable systems based on the method of dispersive deformations of hydrodynamic reductions proposed in [5-6]. This programme is expected to lead to a new class of integrable soliton PDEs with remarkable properties and potential applications.
The project will require basic knowledge of differential equations and differential geometry, as well as familiarity with symbolic computations (Mathematica/Maple).
Programme overview
Main Subject
Mathematics
Degree
PhD
Study Level
PHD
Study Mode
On Campus
Dispersionless Integrable Systems In 2+1 Dimensions PhD
Dispersionless integrable systems occur in a wide range of applications in various areas of pure and applied mathematics. In 2+1 dimensions, there exists an efficient approach to the classification of integrable systems of this kind based on the method of hydrodynamic reductions pioneered by the Loughborough group [1]. This method has lead to extensive classification results within particularly interesting classes revealing deep relations with generalised conformal geometry, theory of hypergeometric functions and modular forms [2-4].
The goal of this project is twofold:
1. Classification of dispersionless integrable systems in 2+1 dimensions with an emphasis on multi-component systems of hydrodynamic type.
2. Reconstruction of dispersive deformations of dispersionless integrable systems based on the method of dispersive deformations of hydrodynamic reductions proposed in [5-6]. This programme is expected to lead to a new class of integrable soliton PDEs with remarkable properties and potential applications.
The project will require basic knowledge of differential equations and differential geometry, as well as familiarity with symbolic computations (Mathematica/Maple).
Admission Requirements
Tuition fees
Domestic
International
Scholarships
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Visual Data Mining on Proteins and Biomedicine Crystallisation PhD
Waste-derived Bioplastics for a Circular and Sustainable Food Packaging Economy PhD
Life Sciences and Medicine (6)
Adaptive and Predictive Computational Modelling of Biomaterials: A Digital Twin Framework for Next-Generation Personalised Healthcare PhD
Adaptive and Predictive Computational Modelling of Biomaterials: A Digital Twin Framework for Next-Generation Personalised Healthcare PhD
Biomarkers of Aging PhD
Biomarkers of Aging PhD
Developing Prescription Guidelines for Passive Heat Therapy PhD
Developing Prescription Guidelines for Passive Heat Therapy PhD
Does Socialised Real-Life Body Exposure Promote Body Image Positivity PhD
Does Socialised Real-Life Body Exposure Promote Body Image Positivity PhD
Energy Dissipation In Human Soft Tissue During Impacts PhD
Energy Dissipation In Human Soft Tissue During Impacts PhD
Natural Sciences (6)
Accelerated Screening and Synthesis of New Chemotherapeutic Agents for Pancreatic Cancer PhD
Accelerated Screening and Synthesis of New Chemotherapeutic Agents for Pancreatic Cancer PhD
Bespoke Organometallic Compounds for Anticancer Studies PhD
Bespoke Organometallic Compounds for Anticancer Studies PhD
Bio-based Sustainable Materials for Autonomous Thermal Management in Wearables PhD
Bio-based Sustainable Materials for Autonomous Thermal Management in Wearables PhD
Biomimmetic Catalytic Asymmetric Synthesis of the Bisorbicillinoids and Related Products PhD
Biomimmetic Catalytic Asymmetric Synthesis of the Bisorbicillinoids and Related Products PhD
Climate and Ecological Transitions Hub Studentship PhD
Climate and Ecological Transitions Hub Studentship PhD
Coherent State Methods in Spectral Asymptotics PhD
Coherent State Methods in Spectral Asymptotics PhD
Computational Modelling of Sustainable Alloys PhD
Designing Classroom Tasks To Improve Students’ Learning Of Mathematics PhD
Developing Novel Antibiofilm Coatings for Sustainable Biofilm-Free Surfaces PhD
Development of Hybrid Microcomb Sources with Topologically Protected Dark Resonances for Simultaneous Classical and Quantum PhD
Development of Novel Bicyclopentanes (BCP) Bioisosteres From Bench Stable [1.1.1]-Propellane Precursors PhD
Digital Twins for Biofilm Management PhD
Dispersionless Integrable Systems In 2+1 Dimensions PhD
Social Sciences and Management (6)
An Evaluation of Erasmus+ Sport Projects and Their Impact on EU Sport Policy Development PhD
An Evaluation of Erasmus+ Sport Projects and Their Impact on EU Sport Policy Development PhD
Climate Change, Work Design and Worker Wellbeing Phd
Climate Change, Work Design and Worker Wellbeing Phd
Communication and Social Change (CSC) Hub Studentship PhD
Communication and Social Change (CSC) Hub Studentship PhD
Enhancing Motivation in Sport and Exercise Contexts PhD
Enhancing Motivation in Sport and Exercise Contexts PhD
Out of School Youth Provision: An Analysis of Funding and Operational Resilience within the Sector PhD
Out of School Youth Provision: An Analysis of Funding and Operational Resilience within the Sector PhD