Viscous Evolution of Magnetized Clumps: a Source for X-ray Flares in Gamma-ray Bursts

**boundary**

**conditions**(with and without a magnetic barrier). Expand abstract.

**boundary**

**condition**through which this mechanism might happen. Regarding various model parameters, we probe for their influence and proceed some key analogies between our model predictions and previous phenomenological estimates, for two different choices of

**boundary**

**conditions**(with and without a magnetic barrier). Our model is remarkably capable of matching flare bolometric and X-ray light-curves, as well as reproducing their statistical properties, such as the ratios between rise and decay time, width parameter and peak time, and the power-law correlation between peak luminosity and peak time. Combining our results with the conclusions of previous studies, we are led to interpret magnetic barrier as a less probable mechanism that might control the evolution of these clumps, especially the later created (or viscously evolved) ones.

5/10 relevant

arXiv

The general fifth-order nonlinear Schr\"odinger equation with nonzero
**boundary** **conditions**: Inverse scattering transform and multisoliton solutions

**boundary**

**conditions**(NZBCs), which can be reduced to several integrable equations. Expand abstract.

**boundary**

**conditions**(NZBCs), which can be reduced to several integrable equations. Firstly, a matrix Riemann-Hilbert problem for the equation with NZBCs at infinity is systematically investigated.Then the inverse problems are solved through the investigation of the matrix Riemann-Hilbert problem. Thus, the general solutions for the potentials, and explicit expressions for the reflection-less potentials are well constructed. Furthermore, the trace formulae and theta

**conditions**are also presented. In particular, we analyze the simple-pole and double-pole solutions for the equation with NZBCs. Finally, the dynamics of the obtained solutions are graphically discussed. These results provided in this work can be useful to enrich and explain the related nonlinear wave phenomena in nonlinear fields.

10/10 relevant

arXiv

Quantum-classical duality for Gaudin magnets with **boundary**

**boundary**and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians $H_j^{\rm G}$ with particles velocities $\dot q_j$ of the classical model all integrals of motion of the latter take zero values. This is the generalization of the quantum-classical duality observed earlier for Gaudin models with periodic

**boundary**

**conditions**and Calogero-Moser models associated with the root system of the type A.

5/10 relevant

arXiv

On a Babu\v{s}ka paradox for polyharmonic operators: spectral stability
and **boundary** homogenization for intermediate problems

**boundary**

**conditions**of intermediate type. Expand abstract.

**boundary**

**conditions**of intermediate type. We identify sharp assumptions on the domain perturbations improving, in the case of polyharmonic operators of higher order,

**conditions**known to be sharp in the case of fourth order operators. The optimality is proved by analysing in detail a

**boundary**homogenization problem, which provides a smooth version of a polyharmonic Babu\v{s}ka paradox.

4/10 relevant

arXiv

The roles of random **boundary** **conditions** in spin systems

**boundary**

**conditions**are one of the simplest realizations of quenched disorder. Expand abstract.

**boundary**

**conditions**are one of the simplest realizations of quenched disorder. They have been used as an illustration of various conceptual issues in the theory of disordered spin systems. Here we review some of these results.

10/10 relevant

arXiv

Inverse scattering transform of an extended nonlinear Schr\"{o}dinger
equation with nonzero **boundary** **conditions** and its multisoliton solutions

**boundary**

**conditions**at infinity is systematically discussed. Expand abstract.

**boundary**conditions, which can model the propagation of waves in dispersive media. Firstly, a matrix Riemann-Hilbert problem for the equation with nonzero

**boundary**

**conditions**at infinity is systematically discussed. Then the inverse problems are solved through the investigation of the matrix Riemann-Hilbert problem. Therefore, the general solutions for the potentials, and explicit expressions for the reflection-less potentials are presented. Furthermore, we construct the simple-pole and double-pole solutions for the equation. Finally, the remarkable characteristics of these solutions are graphically discussed. Our results should be useful to enrich and explain the related nonlinear wave phenomena in nonlinear fields.

10/10 relevant

arXiv

Singular Contact Geometry and Beltrami Fields in Cholesteric Liquid Crystals

**boundary**

**conditions**for singular contact structures, and show we can realise all desired boundary

**condition**s except for normal anchoring on a sphere, where a theorem of Eliashberg and Thurston provides an obstruction to having... Expand abstract.

**boundary**

**conditions**for singular contact structures, and show we can realise all desired

**boundary**

**conditions**except for normal anchoring on a sphere, where a theorem of Eliashberg and Thurston provides an obstruction to having a singular contact structure in the interior. By introducing a singular version of the Lutz twist we show that all contact structures are homotopic within the larger class of singular contact structures. We give applications of our results to the description of topological defects in chiral liquid crystals.

4/10 relevant

arXiv

The p-Laplacian equation in a rough thin domain with terms concentrating
on the **boundary**

**boundary**

**conditions**set in a rough thin domain with concentrated terms on the

**boundary**. We study weak, resonant and high roughness, respectively. In the three cases, we deduce the effective equation capturing the dependence on the geometry of the thin channel and the neighborhood where the concentrations take place.

5/10 relevant

arXiv

**Boundary** Triples and Weyl $m$-functions for Powers of the Jacobi
Differential Operator

**boundary**triples is applied to the classical Jacobi differential operator and its powers in order to obtain the Weyl $m$-function for several self-adjoint extensions with interesting

**boundary**conditions: separated, periodic and those that yield the Friedrichs extension. These matrix-valued Nevanlinna--Herglotz $m$-functions are, to the best knowledge of the author, the first explicit examples to stem from singular higher-order differential equations. The creation of the

**boundary**triples involves taking pieces, determined in a previous paper, of the principal and non-principal solutions of the differential equation and putting them into the sesquilinear form to yield maps from the maximal domain to the

**boundary**space. These maps act like quasi-derivatives, which are usually not well-defined for all functions in the maximal domain of singular expressions. However, well-defined regularizations of quasi-derivatives are produced by putting the pieces of the non-principal solutions through a modified Gram--Schmidt process.

4/10 relevant

arXiv

A Riemann-Hilbert approach to the modified Camassa-Holm equation with
nonzero **boundary** **conditions**

**conditions**across the real axis. Expand abstract.

**conditions**across the real axis. We obtain a representation for the solution of the Cauchy problem for the mCH equation and also a description of certain soliton-type solutions, both regular and non-regular.

8/10 relevant

arXiv