Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term
A nonlinear Schrödinger equation with a higher-order dispersive term describing the propagation of ultrashort femtosecond pulses in optical fibres is considered and is transformed into a second-order nonlinear ordinary differential equation. We investigate the exact travelling wave solutions of the...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/979252 |
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| _version_ | 1832552806240747520 |
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| author | Rui Cao |
| author_facet | Rui Cao |
| author_sort | Rui Cao |
| collection | DOAJ |
| description | A nonlinear Schrödinger equation with a higher-order dispersive term describing the propagation of ultrashort femtosecond pulses in optical fibres is considered and is transformed into a second-order nonlinear ordinary differential equation. We investigate the exact travelling wave solutions of the nonlinear Schrödinger equation using three methods, namely, the auxiliary equation method, the first integral method, and the direct integral method. As a result, Jacobi elliptic function solution, hyperbolic function solution, trigonometric function solution, and rational solution with parameters are obtained successfully. When the parameters are taken as special values, the two known solitary wave solution and periodic wave solution are derived from the solutions obtained. The aim of the paper is to compare the efficiency of the three methods. |
| format | Article |
| id | doaj-art-bce3afc176104920bab628e6b5b20273 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bce3afc176104920bab628e6b5b202732025-02-03T05:57:47ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/979252979252Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive TermRui Cao0Department of Mathematics, Heze University, Heze 274000, ChinaA nonlinear Schrödinger equation with a higher-order dispersive term describing the propagation of ultrashort femtosecond pulses in optical fibres is considered and is transformed into a second-order nonlinear ordinary differential equation. We investigate the exact travelling wave solutions of the nonlinear Schrödinger equation using three methods, namely, the auxiliary equation method, the first integral method, and the direct integral method. As a result, Jacobi elliptic function solution, hyperbolic function solution, trigonometric function solution, and rational solution with parameters are obtained successfully. When the parameters are taken as special values, the two known solitary wave solution and periodic wave solution are derived from the solutions obtained. The aim of the paper is to compare the efficiency of the three methods.http://dx.doi.org/10.1155/2013/979252 |
| spellingShingle | Rui Cao Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term Abstract and Applied Analysis |
| title | Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term |
| title_full | Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term |
| title_fullStr | Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term |
| title_full_unstemmed | Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term |
| title_short | Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term |
| title_sort | travelling wave solutions for nonlinear schrodinger equation with a higher order dispersive term |
| url | http://dx.doi.org/10.1155/2013/979252 |
| work_keys_str_mv | AT ruicao travellingwavesolutionsfornonlinearschrodingerequationwithahigherorderdispersiveterm |