The Luby Transform (LT) codes are the first practical realization of fountain codes. LT codes were designed for efficient use over erasure channels. However, the degree distributions designed for the Binary Erasure Channel (BEC), such as the Robust Soliton Distribution (RSD) which are asymptotically and universally optimal over the BEC, are not optimal over noisy channels. Research has been don...

in a typical solitonic distribution, the soliton density is distributed over the entire moleculeand the present work shows how its density can be decomposed into solitonic and antisolitoniccomponents. it is found that there exists a unique electron as soliton over the anionicnanoconductor, while there are many other solitons and antisolitons. the solitonic states are furtherdecomposed to the ca...

In a typical solitonic distribution, the soliton density is distributed over the entire moleculeand the present work shows how its density can be decomposed into solitonic and antisolitoniccomponents. It is found that there exists a unique electron as soliton over the anionicnanoconductor, while there are many other solitons and antisolitons. The solitonic states are furtherdecomposed to the ca...

We provide analytical functions approximating e −x 2 dx, the basis of which is the kink soliton and which are both accurate (error < 0.2%) and simple. We demonstrate our results with some applications, particularly to the generation of Gaussian random fields.

A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS-Kaup-Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of...

We study Ricci solitons in Lorentzian α-Sasakian manifolds. It is shown that a symmetric parallel second order covariant tensor in a Lorentzian α-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that if LV g + 2S is parallel, V is a given vector field then (g, V ) is Ricci soliton. Further, by virtue of this result Ricci solitons for (2n + 1)-dimensional Lor...

We consider the Ricci flow for simply connected nilmanifolds, which translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner product with respect to time and the evolution of structure constants with respect to time, as well as the evolution of these quantities modulo rescaling. We set up systems of O.D.E.’s for some of these flows and des...

We prove the following results: (i) A Sasakian metric as a nontrivial Ricci soliton is null η-Einstein, and expanding. Such a characterization permits to identify the Sasakian metric on the Heisenberg group H as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an ηEinstein contact metric manifold M has a vector field V leaving the structure tensor and the scalar curvatur...

We show that a left-invariant metric g on a nilpotent Lie group N is a soliton metric if and only if a matrix U and vector v associated the manifold (N, g) satisfy the matrix equation Uv = [1], where [1] is a vector with every entry a one. We associate a generalized Cartan matrix to the matrix U and use the theory of Kac-Moody algebras to analyze the solution spaces for such linear systems. We ...

We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations. The latter equations are both known to be integrable, and admit peaked soliton (peakon) solutions with discontinuous derivatives at the peaks. A combination of a reciprocal transformation wi...