Add to ORKGThis thesis is concerned with the relationship between integrable Hamiltonian partial differential equations and geometric structures on the manifold in which the dependent variables take their values. Chapters 1 and 2 are introductory chapters, and as such contain no original material. Chapter 1 covers some basic material from the theory of integrable systems, including the Hamiltonian formalism for PDE's, the concept of a bi-Hamiltonian system, and the dispersionless Lax equation. Chapter 2 is about Frobenius manifolds. It explains their relationship to the WDVV equations of topological quantum field theory, and how they form part of the theory of integrable systems via both the deformed Levi-Civita connection and a flat pencil of metri...
We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonl...
The plan of the work is the following: ² In Chapter 1 we recall, basically from [16] and [14], the ...
The plan of the work is the following: ² In Chapter 1 we recall, basically from [16] and [14], the ...
This thesis is concerned with the relationship between integrable Hamiltonian partial differential e...
This thesis is concerned with the relationship between integrable Hamiltonian partial differential e...
Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynam...
The notion of integrability will often extend from systems with scalar-valued fields to systems with...
This volume describes and fully illustrates both the theory and applications of integrable Hamiltoni...
Preface In the past decades now a famous class of evolution equations has been discovered and intens...
Preface In the past decades now a famous class of evolution equations has been discovered and intens...
Preface In the past decades now a famous class of evolution equations has been discovered and intens...
Preface In the past decades now a famous class of evolution equations has been discovered and intens...
The paper surveys open problems and questions related to different aspects of integrable systems wit...
The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. ...
Hamiltonian system on a Poisson manifold M is called integrable if it possesses sufficiently many co...
We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonl...
The plan of the work is the following: ² In Chapter 1 we recall, basically from [16] and [14], the ...
The plan of the work is the following: ² In Chapter 1 we recall, basically from [16] and [14], the ...
This thesis is concerned with the relationship between integrable Hamiltonian partial differential e...
This thesis is concerned with the relationship between integrable Hamiltonian partial differential e...
Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynam...
The notion of integrability will often extend from systems with scalar-valued fields to systems with...
This volume describes and fully illustrates both the theory and applications of integrable Hamiltoni...
Preface In the past decades now a famous class of evolution equations has been discovered and intens...
Preface In the past decades now a famous class of evolution equations has been discovered and intens...
Preface In the past decades now a famous class of evolution equations has been discovered and intens...
Preface In the past decades now a famous class of evolution equations has been discovered and intens...
The paper surveys open problems and questions related to different aspects of integrable systems wit...
The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. ...
Hamiltonian system on a Poisson manifold M is called integrable if it possesses sufficiently many co...
We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonl...
The plan of the work is the following: ² In Chapter 1 we recall, basically from [16] and [14], the ...
The plan of the work is the following: ² In Chapter 1 we recall, basically from [16] and [14], the ...