Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic Potentials
The advantageous Green’s function method that originally has been developed for nonhomogeneous linear equations has been recently extended to nonlinear equations by Frasca. This article is devoted to rigorous and numerical analysis of some second-order differential equations new nonlinearities by me...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/7179160 |
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| author | Asatur Zh. Khurshudyan |
| author_facet | Asatur Zh. Khurshudyan |
| author_sort | Asatur Zh. Khurshudyan |
| collection | DOAJ |
| description | The advantageous Green’s function method that originally has been developed for nonhomogeneous linear equations has been recently extended to nonlinear equations by Frasca. This article is devoted to rigorous and numerical analysis of some second-order differential equations new nonlinearities by means of Frasca’s method. More specifically, we consider one-dimensional wave equation with quadratic and hyperbolic nonlinearities. The case of exponential nonlinearity has been reported earlier. Using the method of generalized separation of variables, it is shown that a hierarchy of nonlinear wave equations can be reduced to second-order nonlinear ordinary differential equations, to which Frasca’s method is applicable. Numerical error analysis in both cases of nonlinearity is carried out for various source functions supporting the advantage of the method. |
| format | Article |
| id | doaj-art-e63e0e7622f547a5a6c42d0f11e29ce4 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-e63e0e7622f547a5a6c42d0f11e29ce42025-08-20T03:26:04ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/71791607179160Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic PotentialsAsatur Zh. Khurshudyan0Department of Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia, 24B Baghramyan Ave., 0019 Yerevan, ArmeniaThe advantageous Green’s function method that originally has been developed for nonhomogeneous linear equations has been recently extended to nonlinear equations by Frasca. This article is devoted to rigorous and numerical analysis of some second-order differential equations new nonlinearities by means of Frasca’s method. More specifically, we consider one-dimensional wave equation with quadratic and hyperbolic nonlinearities. The case of exponential nonlinearity has been reported earlier. Using the method of generalized separation of variables, it is shown that a hierarchy of nonlinear wave equations can be reduced to second-order nonlinear ordinary differential equations, to which Frasca’s method is applicable. Numerical error analysis in both cases of nonlinearity is carried out for various source functions supporting the advantage of the method.http://dx.doi.org/10.1155/2018/7179160 |
| spellingShingle | Asatur Zh. Khurshudyan Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic Potentials Advances in Mathematical Physics |
| title | Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic Potentials |
| title_full | Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic Potentials |
| title_fullStr | Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic Potentials |
| title_full_unstemmed | Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic Potentials |
| title_short | Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic Potentials |
| title_sort | nonlinear green s functions for wave equation with quadratic and hyperbolic potentials |
| url | http://dx.doi.org/10.1155/2018/7179160 |
| work_keys_str_mv | AT asaturzhkhurshudyan nonlineargreensfunctionsforwaveequationwithquadraticandhyperbolicpotentials |