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The uniqueness and existence of solutions for the 3D Helmholtz equation in a step‐index waveguide with unbounded perturbation
Author(s) -
Liu Lihan,
Qin Yuehai,
Xu Yongzhi,
Zhao Yuqiu
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1620
Subject(s) - helmholtz equation , uniqueness , mathematics , perturbation (astronomy) , helmholtz free energy , mathematical analysis , homogeneous , waveguide , physics , optics , boundary value problem , quantum mechanics , combinatorics
In this paper, we study the 3D Helmholtz equation in a step‐index waveguide with unbounded perturbation, allowing the presence of guided waves. Our assumptions on the perturbed and source terms are too few. On the basis of the Green's function for the 3D homogeneous Helmholtz equation in a step‐index waveguide without perturbation, we introduce a generalized (out‐going) Sommerfeld–Rellich radiation condition, and then we prove the uniqueness and existence of solutions for the studied 3D Helmholtz equation satisfying our radiation condition. Copyright © 2012 John Wiley & Sons, Ltd.