We consider the problem of absence of backscattering in the transport of Manakov solitons on a line. The concept of transparent boundary conditions is used for modeling the reflectionless propagation of Manakov vector solitons in a one-dimensional domain. Artificial boundary conditions that ensure the absence of backscattering are derived and their numerical implementation is demonstrated.
We consider the reflectionless transport of sine-Gordon solitons on a line. Transparent boundary conditions for the sine-Gordon equation on a line are derived using the so-called potential approach. Our numerical implementation of these novel boundar
y conditions proves the absence of the backscattering in transmission of sine-Gordon solitons through the boundary of the considered finite domains.
The interaction of a quantum field with a background containing a Dirac delta function with support on a surface of codimension 1 represents a particular kind of matching conditions on that surface for the field. In this article we show that the worl
dline formalism can be applied to this model. We obtain the asymptotic expansion of the heat-kernel corresponding to a scalar field on $mathbb{R}^{d+1}$ in the presence of an arbitrary regular potential and subject to this kind of matching conditions on a flat surface. We also consider two such surfaces and compute their Casimir attraction due to the vacuum fluctuations of a massive scalar field weakly coupled to the corresponding Dirac deltas.
The two time-dependent Schrodinger equations in a potential V(s,u), $u$ denoting time, can be interpreted geometrically as a moving interacting curves whose Fermi-Walker phase density is given by -dV/ds. The Manakov model appears as two moving intera
cting curves using extended da Rios system and two Hasimoto transformations.
It has been conjectured that the defocusing nonlinear Schrodinger (NLS) equation on the half-line does not admit solitons. We give a proof of this conjecture.
In this paper an effective integrable non-linear model describing the electron spin dynamics in a deformable helical molecule with weak spin-orbit coupling is presented. Non-linearity arises from the electron-lattice interaction and it enables the fo
rmation of a variety of stable solitons such as bright solitons, breathers and rogue waves, all of them presenting well defined spin projection onto the molecule axis. A thorough study of the soliton solutions is presented and discussed.
K.K. Sabirov
,J.R. Yusupov
,M.M. Aripov
.
(2021)
.
"Reflectionless propagation of Manakov solitons on a line:A model based on the concept of transparent boundary conditions"
.
Davron Matrasulov
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