Nonlinear Goubau line: analytical–numerical approaches and new propagation regimes

Smolkin, Eugene; Shestopalov, Yury

doi:10.1080/09205071.2017.1317036

Cited by 21 publications

(8 citation statements)

References 12 publications

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“…The proposed solution technique is justified using classical results of the theory of ordinary differential equations concerning the existence and uniqueness of the solution to the Cauchy problem and continuous dependence of the solution on parameters (see Smolkin & Shestopalov, ).…”

Section: Numerical Methods and Resultsmentioning

confidence: 99%

“…Using the transmission condition on the boundary ρ = r 0 , we obtain the following dispersion equation

normalΔ ((), F_{I}, F_{R}) \equiv u ((), r_{0}) = 0,

where

normalΔ ((), F_{I}, F_{R})

is determined explicitly and quantity

u ((), r_{0})

is obtained from the solution to the Cauchy problem for fixed values of F I and F R (see Smolkin & Shestopalov, ).…”

Section: Numerical Methods and Resultsmentioning

confidence: 99%

“…The case of nonlinear filling still constitutes an unsolved problem. A progress here is associated with recently developed techniques (see Smirnov & Smolkin, ; Smolkin & Shestopalov, ; Valovik & Smolkin, ; and Smolkin & Valovik, ) for the analysis of nonlinear boundary value problems for the Maxwell's and Helmholtz equations.…”

Section: Introductionmentioning

confidence: 99%

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Diffraction of a TE‐Polarized Wave by a Nonlinear Goubau Line

2019

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The diffraction of a cylindrical wave by a nonlinear metal‐dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented.

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Section: Numerical Methods and Resultsmentioning

confidence: 99%

“…Using the transmission condition on the boundary ρ = r 0 , we obtain the following dispersion equation

normalΔ ((), F_{I}, F_{R}) \equiv u ((), r_{0}) = 0,

where

normalΔ ((), F_{I}, F_{R})

is determined explicitly and quantity

u ((), r_{0})

is obtained from the solution to the Cauchy problem for fixed values of F I and F R (see Smolkin & Shestopalov, ).…”

Section: Numerical Methods and Resultsmentioning

confidence: 99%

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Diffraction of a TE‐Polarized Wave by a Nonlinear Goubau Line

2019

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“…Using the same technique as in Smolkin and Shestopalov (2017), we obtain an integral representation of solution u ( s ) to Equation for s ∈ [0, r ]:

u false(s false) = - α true \int_{0}^{r} G false(ρ, s false) ρ u^{3} false(ρ false) d ρ + f false(s false),

where

f false(s false) = - r u false(r false) G^{'} false(r, s false) = u false(r false) \frac{J_{1} false(κ s false)}{J_{1} false(κ r false)}

.…”

Section: Nonlinear Integral Equationmentioning

confidence: 99%

“…This framework has not been addressed in the literature, to the best of our knowledge. A background study concerning nonlinear guided waves in media with Kerr and Kerr‐like nonlinearities can be found in Smirnov and Smolkin (2018), Smolkin and Shestopalov (2017), Smolkin and Valovik (2015), and Smirnov et al (2019). In papers (Smirnov et al, 2014; Smolkin, 2017; Smolkin et al, 2017; Smolkin & Shestopalov, 2015; Smolkin & Valovik, 2012) numerical study of the surface wave propagation in layered nonlinear dielectric and metal‐dielectric waveguides is performed.…”

Section: Introductionmentioning

confidence: 99%

Surface Waves in a Nonlinear Metamaterial Rod

2020

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We consider propagation of surface Transverse Electric (TE) waves in a rod filled with nonlinear metamaterial medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear surface TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.

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Numerical Study of the Azimuthal Symmetric Hybrid Waves in a Nonlinear Cylindrical Waveguide

Smolkin

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Nonlinear Goubau line: analytical–numerical approaches and new propagation regimes

Cited by 21 publications

References 12 publications

Diffraction of a TE‐Polarized Wave by a Nonlinear Goubau Line

Diffraction of a TE‐Polarized Wave by a Nonlinear Goubau Line

Surface Waves in a Nonlinear Metamaterial Rod

Numerical Study of the Azimuthal Symmetric Hybrid Waves in a Nonlinear Cylindrical Waveguide

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