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Dispersionless Integrable Systems In 2+1 Dimensions PhD
Loughborough University, Loughborough, United Kingdom
# 201-250QS Subject Rankings
36 monthsProgram duration
21,500 Tuition Fee/year
01 Apr, 2025Application Deadline
Program 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...
Read more
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).
Read lessProgram 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...
Read more
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).
Read lessAdmission Requirements
Tuition Fee
Domestic Students
International Students
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QS subject rankings
Subject: Mathematics
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Social Sciences and Management (5)
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