Add to ORKG2010 Mathematics Subject Classification: 35Q35, 37K10.We consider the μCH equation which arises as an asymptotic rotator equation in a liquid crystal with a preferred direction if one takes into account the reciprocal action of dipoles on themselves. This equation is closely related to the periodic Camassa–Holm and the Hunter-Saxton equations. The μCH equation is also integrable and bi-Hamiltonian, that is, it is Hamiltonian with respect to two compatible Poisson brackets. We give a set of conjugated variables for both brackets.This work is partially supported by grant 193/2011 of Sofia University
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We prove that all Hopf bifurcations in the Nicholson’s blowfly equation are supercritical as we incr...
In contrast to the usual treatment (see e.g. J.J. Duistermaat [3]) convolution groups are constructe...
An overview over some aspects of the Fucik spectrum are given, in particular in the situation when t...
A class of equations describing the geodesic flow for a right-invariant metric on the group of diffe...
The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently...
AbstractWe present a simple method to calculate the Stokes matrix for the quantum cohomology of the ...
In this paper we study the use of energy-conserving methods, in the class of Hamiltonian Boundary Va...
We prove the persistence of finite dimensional invariant tori associated with the dfocusing nonlinea...
We analyse the famous Baxter's $T-Q$ equations for $XXX$ ($XXZ$) spin chain and show that apart from...
We prove that the dynamical system charaterized by the Hamiltonian H = \lambda N \sum_{j}^{N} p_j + ...
AbstractThe purpose of this paper is two-fold. Firstly, we will give some parabolic-like conditions ...
We give an overview of recent results obtained in joint works with Dubrovin and Guzzetti (Helix stru...
We prove existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as per...
summary:The oscillation of the solutions of linear parabolic differential equations with deviating a...
We provide a mathematical account of the recent Physical Reviews Letter by Tarnopolsky--Kruchkov--Vi...
We prove that all Hopf bifurcations in the Nicholson’s blowfly equation are supercritical as we incr...
In contrast to the usual treatment (see e.g. J.J. Duistermaat [3]) convolution groups are constructe...
An overview over some aspects of the Fucik spectrum are given, in particular in the situation when t...