A class of localized soliton and fractal pattern solutions of the (2 + 1)-dimensional modified dispersive long wave model

2020 ◽  
Vol 95 (8) ◽  
pp. 085219 ◽  
Author(s):  
Mst Shekha Khatun ◽  
Md Fazlul Hoque ◽  
Md Azizur Rahman
Keyword(s):  
Wave Motion ◽  
2016 ◽  
Vol 65 ◽  
pp. 156-174 ◽  
Author(s):  
R.M. Vargas-Magaña ◽  
P. Panayotaros

MRS Advances ◽  
2019 ◽  
Vol 4 (11-12) ◽  
pp. 667-674 ◽  
Author(s):  
Rachel N. Evans ◽  
Seth R. Calhoun ◽  
Jonathan R. Brescia ◽  
Justin W. Cleary ◽  
Evan M. Smith ◽  
...  

ABSTRACTMetal–insulator–metal (MIM) resonant absorbers comprise a conducting ground plane, a dielectric of thickness t, and thin separated metal top-surface structures of dimension l. The fundamental resonance wavelength is predicted by an analytic standing-wave model based on t, l, and the dielectric refractive index spectrum. For the dielectrics SiO2, AlN, and TiO2, values for l of a few microns give fundamental resonances in the 8-12 μm long-wave infrared (LWIR) wavelength region. Agreement with theory is better for t/l exceeding 0.1. Harmonics at shorter wavelengths were already known, but we show that there are additional resonances in the far-infrared 20 - 50 μm wavelength range in MIM structures designed to have LWIR fundamental resonances. These new resonances are consistent with the model if far-IR dispersion features in the index spectrum are considered. LWIR fundamental absorptions are experimentally shown to be optimized for a ratio t/l of 0.1 to 0.3 for SiO2- and AlN-based MIM absorbers, respectively, with TiO2-based MIM optimized at an intermediate ratio.


2015 ◽  
Vol 9 ◽  
pp. 6747-6756
Author(s):  
Alex M. Montes ◽  
Ricardo Cordoba

Author(s):  
M Faquir ◽  
M.A Manna ◽  
A Neveu

The dynamics of a nonlinear and dispersive long surface capillary-gravity wave model equation is studied analytically in its short-wave limit. We exhibit its Lax pair and some non-trivial conserved quantities. Through a change of functions, an unexpected connection between this classical surface water-wave model and the sine-Gordon (or sinh-Gordon) equation is established. Numerical and analytical studies show that in spite of integrability their solutions can develop singularities and multivaluedness in finite time. These features can be traced to the fact that the surface tension term in the energy involves second-order derivatives. It would be interesting to see in an experiment whether such singularities actually appear, for which surface tension would be specifically responsible.


Author(s):  
H.-H. Dai ◽  
J. Kaplunov ◽  
D. A. Prikazchikov

The paper deals with the three-dimensional problem in linear isotropic elasticity for a coated half-space. The coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long-wave limit. An explicit model is derived for the surface wave using the perturbation technique, along with the theory of harmonic functions and Radon transform. The model consists of three-dimensional ‘quasi-static’ elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two-dimensional hyperbolic equation singularly perturbed by a pseudo-differential (or integro-differential) operator. The latter equation governs dispersive surface wave propagation, whereas the elliptic equations describe spatial decay of displacements and stresses. As an illustration, the dynamic response is calculated for impulse and moving surface loads. The explicit analytical solutions obtained for these cases may be used for the non-destructive testing of the thickness of the coating and the elastic moduli of the substrate.


2018 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Omid Nikan ◽  
◽  
Seyedeh Mahboubeh Molavi-Arabshai ◽  
Hossein Jafari ◽  
◽  
...  

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