Iryna Karpenko
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View article: Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems
Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems Open
We consider the Riemann–Hilbert (RH) approach to the construction of periodic finite-band solutions to the focusing nonlinear Schrödinger (NLS) equation. An RH problem for the solution of the finite-band problem has been recently derived v…
View article: Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems
Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems Open
We consider the Riemann--Hilbert (RH) approach to the construction of periodic finite-band solutions to the focusing nonlinear Schrödinger (NLS) equation. An RH problem for the solution of the finite-band problem has been recently derived …
View article: A Riemann–Hilbert approach to the modified Camassa–Holm equation with step-like boundary conditions
A Riemann–Hilbert approach to the modified Camassa–Holm equation with step-like boundary conditions Open
The paper aims at developing the Riemann–Hilbert (RH) approach for the modified Camassa–Holm (mCH) equation on the line with non-zero boundary conditions, in the case when the solution is assumed to approach two different constants at diff…
View article: Linear expand-contract plasticity of ellipsoids revisited
Linear expand-contract plasticity of ellipsoids revisited Open
This work is aimed to describe linearly expand-contract plastic ellipsoids given via quadratic form of a bounded positively defined self-adjoint operator in terms of its spectrum.Let $Y$ be a metric space and $F\colon Y\to Y$ be a map. $F$…
View article: Linear Expand-Contract Plasticity of Ellipsoids Revisited
Linear Expand-Contract Plasticity of Ellipsoids Revisited Open
This work is aimed to describe linear expand-contract plastic ellipsoids given via quadratic form of a bounded positively defined self-adjoint operator in terms of its spectrum.
View article: A Riemann-Hilbert approach to the modified Camassa-Holm equation with\n step-like boundary conditions
A Riemann-Hilbert approach to the modified Camassa-Holm equation with\n step-like boundary conditions Open
The paper aims at developing the Riemann-Hilbert (RH) approach for the\nmodified Camassa-Holm (mCH) equation on the line with non-zero boundary\nconditions, in the case when the solution is assumed to approach two different\nconstants at d…
View article: The modified Camassa-Holm equation on a nonzero background: large-time asymptotics for the Cauchy problem
The modified Camassa-Holm equation on a nonzero background: large-time asymptotics for the Cauchy problem Open
This paper deals with the Cauchy problem for the modified Camassa-Holm (mCH) equation \begin{alignat*}{4} &m_t+\left((u^2-u_x^2)m\right)_x=0,&\quad&m:= u-u_{xx},&\quad&t>0,&\;&-\infty0$), where the leading asymptotic term of the deviation …
View article: A Riemann–Hilbert approach to the modified Camassa–Holm equation with nonzero boundary conditions
A Riemann–Hilbert approach to the modified Camassa–Holm equation with nonzero boundary conditions Open
This paper aims at developing the Riemann–Hilbert problem approach to the modified Camassa–Holm (mCH) equation in the case when the solution is assumed to approach a non-zero constant at both infinities of the space variable. In this case,…
View article: Nonlinear Fourier Spectrum Characterization of Time-Limited Signals
Nonlinear Fourier Spectrum Characterization of Time-Limited Signals Open
Addressing the optical communication systems employing the nonlinear Fourier transform (NFT) for the data modulation/demodulation, we provide an explicit proof for the properties of the signals emerging in the so-called b-modulation method…
View article: On the rigorous justification of b-modulation method and inclusion of discrete eigenvalues
On the rigorous justification of b-modulation method and inclusion of discrete eigenvalues Open
Addressing the optical communication systems employing the nonlinear Fourier transform (NFT) for the data modulation/demodulation, we provide the explicit proof for the properties of the signals emerging in the so-called b-modulation metho…
View article: INNOVATIVE TECHNOLOGIES IN THE DEVELOPMENT OF TOURISM IN UKRAINE AND THE WORLD
INNOVATIVE TECHNOLOGIES IN THE DEVELOPMENT OF TOURISM IN UKRAINE AND THE WORLD Open
Національний університет харчових технологій ІННОВАЦІЙНІ ТЕХНОЛОГІї У СФЕРІ РОЗВИТКУ ТУРИЗМУ В УКРАїНІ ТА У СВІТІАнотація.Інновації є ключовими елементами, які стимулюють економіку у
View article: On sufficient conditions for a polynomial to be sign-independently hyperbolic or to have real separated zeros
On sufficient conditions for a polynomial to be sign-independently hyperbolic or to have real separated zeros Open
The well-known Hutchinson's theorem states that if P be a polynomial with positive coefficients, P(x) = ∑ n k=0 a k x k , and4 for k = 2,3,... ,n , then all the zeros of P are real.We obtain sufficient conditions for a real polynomial to b…