n-order perturbative solution of the inhomogeneous wave equation
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| Natura: | Artículo científico |
| Lingua: | en |
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Sociedad Mexicana de Física A.C.
2008
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| _version_ | 1876486406043336704 |
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| author | H. Yépez-Martínez |
| author_facet | H. Yépez-Martínez |
| contents | n-order perturbative solution of the inhomogeneous wave equation H. Yépez-Martínez A. Porta E. Yépez Física, Astronomía y Matemáticas wave propagation Inhomogeneous media perturbation theory The exact solution of the inhomogeneous wave equation in one dimension, when the square of the velocity is a linear function of the position, can be written in terms of Bessel functions of the first kind. We use this solution as the zero order approximation for a perturbation expansion and apply it to the case when the square of the velocity can be written as a polynomial in the position. The first and second order perturbation terms, corresponding to quadratic and cubic terms for the square of the velocity, are obtained. A closed formula for the n-order correction in terms of integrals of the Bessel functions of the first kind was also explicitly obtained, this expression can be solved analytically for the first and second order corrections and numerically for higher terms. 2008 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57028302003 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.54 |
| format | Artículo científico |
| id | redalyc_57028302003 |
| institution | Redalyc |
| language | en |
| publishDate | 2008 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | n-order perturbative solution of the inhomogeneous wave equation H. Yépez-Martínez Física, Astronomía y Matemáticas wave propagation Inhomogeneous media perturbation theory n-order perturbative solution of the inhomogeneous wave equation H. Yépez-Martínez A. Porta E. Yépez Física, Astronomía y Matemáticas wave propagation Inhomogeneous media perturbation theory The exact solution of the inhomogeneous wave equation in one dimension, when the square of the velocity is a linear function of the position, can be written in terms of Bessel functions of the first kind. We use this solution as the zero order approximation for a perturbation expansion and apply it to the case when the square of the velocity can be written as a polynomial in the position. The first and second order perturbation terms, corresponding to quadratic and cubic terms for the square of the velocity, are obtained. A closed formula for the n-order correction in terms of integrals of the Bessel functions of the first kind was also explicitly obtained, this expression can be solved analytically for the first and second order corrections and numerically for higher terms. 2008 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57028302003 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.54 |
| title | n-order perturbative solution of the inhomogeneous wave equation |
| topic | Física, Astronomía y Matemáticas wave propagation Inhomogeneous media perturbation theory |
| url | https://www.redalyc.org/articulo.oa?id=57028302003 |