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Generalized Helmholtz equation
Selecciones Matemáticas, 2019 In this paper we introduce the generalized Helmholtz equation and present explicit solutions to this generalized Helmholtz equation, these solutions depend on three holomorphic functions.
Carlos C. Riveros, Armando V. Corro
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Boundary regularized integral equation formulation of the Helmholtz equation in acoustics [PDF]
Royal Society Open Science, 2015 A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically.
Qiang Sun +3 more
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Some properties and applications of the Teodorescu operator associated to the Helmholtz equation [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we first define the Teodorescu operator T ψ , α $T_{\psi,\alpha }$ related to the Helmholtz equation and discuss its properties in quaternion analysis.
Pei Yang, Liping Wang, Long Gao
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An exact transverse Helmholtz equation [PDF]
Journal of the Optical Society of America A, 2009 We derive an exact equation for the transverse component of the electric field propagating along a given longitudinal z direction in the presence of an isotropic refractive-index distribution n(x,y)
Crosignani, Bruno +2 more
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On a fourth order nonlinear Helmholtz equation [PDF]
Journal of the London Mathematical Society, 2018 In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $\Delta^2 u -\beta \Delta u + \alpha u= \Gamma|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $\Gamma$.
Abramowitz M. +11 more
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A robust approach for computing solutions of fractional-order two-dimensional Helmholtz equation [PDF]
Scientific ReportsThe Helmholtz equation plays a crucial role in the study of wave propagation, underwater acoustics, and the behavior of waves in the ocean environment. The Helmholtz equation is also used to describe propagation through ocean waves, such as sound waves ...
Muhammad Nadeem +3 more
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Coupled Helmholtz equations: Chirped solitary waves [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021 We investigate the existence and stability properties of chirped gray and anti-dark solitary waves within the framework of a coupled cubic nonlinear Helmholtz equation in the presence of self-steepening and a self-frequency shift. We show that for a particular combination of self-steepening and a self-frequency shift, there is not only chirping but ...
Naresh Saha, Barnana Roy, Avinash Khare
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Mathematics, 2023 In this work, it is shown that the geometry of a gravity field generated by a spheroid with low eccentricity can be described with the help of a newly modified Helmholtz equation.
Gerassimos Manoussakis
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Journal of Mathematics, 2022 The Quasi-Reversibility Regularization Method (Q-RRM) provides stable approximate solution of the Cauchy problem of the Helmholtz equation in the Hilbert space by providing either additional information in the Laplace-type operator in the Helmholtz ...
Benedict Barnes +3 more
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Continuous operator method application for direct and inverse scattering problems
Журнал Средневолжского математического общества, 2021 We describe the continuous operator method for solution nonlinear operator equations and discuss its application for investigating direct and inverse scattering problems.
Boykov Ilya V. +3 more
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