Concept

Integrable system

Related publications (129)

Asymmetric breaking size-segregation waves in dense granular free-surface flows

Debris and pyroclastic flows often have bouldery flow fronts, which act as a natural dam resisting further advance. Counter intuitively, these resistive fronts can lead to enhanced run-out, because they can be shouldered aside to form static levees that se ...

Cambridge University Press2016

Harmonization of chaos into a soliton in Kerr frequency combs

Tobias Kippenberg

Dissipative Kerr solitons have paved the way to broadband and fully coherent optical frequency combs in microresonators. Here, we demonstrate numerically that slow frequency tuning of the pump laser in conjunction with phase or amplitude modulation corresp ...

Optical Society of America2016

Raman Self-Frequency Shift of Dissipative Kerr Solitons in an Optical Microresonator

Tobias Kippenberg, Victor Brasch, Michail Zervas, Michael Wolfgang Geiselmann, Maxim Karpov, Hairun Guo, Martin Hubert Peter Pfeiffer, Arne Kordts

We experimentally observed the Raman-induced self-frequency shift of high-intensity dissipative Kerr solitons in high-Q silicon nitride microresonators. The Raman redshift is linearly dependent on the pump-frequency-detuning, associated with the tunability ...

Ieee2016

Bringing short-lived dissipative Kerr soliton states in microresonators into a steady state

Tobias Kippenberg, Victor Brasch, Michael Wolfgang Geiselmann, Martin Hubert Peter Pfeiffer

Dissipative Kerr solitons have recently been generated in optical microresonators, enabling ultrashort optical pulses at microwave repetition rates, that constitute coherent and numerically predictable Kerr frequency combs. However, the seeding and excitat ...

Optical Society of America2016

MATHICSE Technical Report : Perturbation of higher-order singular values

Daniel Kressner, André Uschmajew

The higher-order singular values for a tensor of order d are defined as the singular values of the d different matricizations associated with the multilinear rank. When d≥3, the singular values are generally different for different matricizations but not c ...

MATHICSE2016

Study on the detuning-dependent properties of a temporal dissipative Kerr soliton in an optical microresonator

Tobias Kippenberg, Erwan Guillaume Albert Lucas, John David Jost

Temporal dissipative Kerr solitons in a continuous-wave laser-driven nonlinear optical microresonator enable compact, high-repetition rate sources of ultrashort pulses and coherent broadband optical frequency combs. A central parameter in the soliton forma ...

2016

Algebraic Complete Integrability of the Bloch-Iserles System

Tudor Ratiu

The goal of this paper is the proof of the algebraic complete integrability of the Bloch-Iserles Hamiltonian system [5]. This result was conjectured in [4], based on its validity in certain special cases. ...

Oxford University Press2015

Lagrangian Reductions and Integrable Systems in Condensed Matter

Tudor Ratiu, François Gay-Balmaz

We consider a general approach for the process of Lagrangian and Hamiltonian reduction by symmetries in chiral gauge models. This approach is used to show the complete integrability of several one dimensional texture equations arising in liquid Helium phas ...

Springer2015

Integrable Systems of Neumann Type

Tudor Ratiu

We construct families of integrable systems that interpolate between -dimensional harmonic oscillators and Neumann systems. This is achieved by studying a family of integrable systems generated by the Casimir functions of the Lie algebra of real skew-symme ...

Springer Verlag2015

Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields

Maria Colombo

In this paper we provide a complete analogy between the Cauchy-Lipschitz and the DiPerna-Lions theories for ODE's, by developing a local version of the DiPerna-Lions theory. More precisely, we prove the existence and uniqueness of a maximal regular flow fo ...

2015

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