Journal of Nonlinear Mathematical Physics

Volume 11, Issue Supplement 1, October 2004, Pages 110 - 115

Nonlinear Wave Equation in Special Coordinates

Authors
Alexander Shermenev
Corresponding Author
Alexander Shermenev
Available Online 1 October 2004.
DOI
https://doi.org/10.2991/jnmp.2004.11.s1.14How to use a DOI?
Abstract
Some classical types of nonlinear periodic wave motion are studied in special coodinates. In the case of cylinder coordinates, the usual perturbation techniques leads to the overdetermined systems of linear algebraic equations for unknown coefficients whose compatibility is key step of the investigation. Their solutions give solutions to the nonlinear wave equation which are periodic in time and found with the same accuracy as the nonlinear wave equation is derived. Expanding the potential for wave motion in Fourier series, we express explicitly the coefficients of the first two harmonics as quadratic polynomials of Bessel functions. One may speculate that the obtained expressions are only the first two terms of an exact solution to the nonlinear wave equations.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
11 - Supplement 1
Pages
110 - 115
Publication Date
2004/10
ISBN
91-974824-2-0
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2004.11.s1.14How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Alexander Shermenev
PY  - 2004
DA  - 2004/10
TI  - Nonlinear Wave Equation in Special Coordinates
JO  - Journal of Nonlinear Mathematical Physics
SP  - 110
EP  - 115
VL  - 11
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.s1.14
DO  - https://doi.org/10.2991/jnmp.2004.11.s1.14
ID  - Shermenev2004
ER  -