Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation
This paper is concerned with periodic traveling wave solutions of the forced generalized nearly concentric Korteweg-de Vries equation in the form of (uη+u/(2η)+[f(u)]ξ+uξξξ)ξ+uθθ/η2=h0. The authors first convert this equation into a forced generalized Kadomtsev-Petviashvili equation, (ut+[f(u)]x+ux...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171200004336 |
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| author | Kenneth L. Jones Xiaogui He Yunkai Chen |
| author_facet | Kenneth L. Jones Xiaogui He Yunkai Chen |
| author_sort | Kenneth L. Jones |
| collection | DOAJ |
| description | This paper is concerned with periodic traveling wave solutions of
the forced generalized nearly concentric Korteweg-de Vries equation
in the form of (uη+u/(2η)+[f(u)]ξ+uξξξ)ξ+uθθ/η2=h0. The authors first convert this equation into a forced generalized Kadomtsev-Petviashvili equation, (ut+[f(u)]x+uxxx)x+uyy=h0, and then to a nonlinear
ordinary differential equation with periodic boundary conditions.
An equivalent relationship between the ordinary differential
equation and nonlinear integral equations with symmetric kernels is
established by using the Green's function method. The integral
representations generate compact operators in a Banach space of
real-valued continuous functions. The Schauder's fixed point
theorem is then used to prove the existence of nonconstant
solutions to the integral equations. Therefore, the existence of
periodic traveling wave solutions to the forced generalized KP
equation, and hence the nearly concentric KdV equation, is proved. |
| format | Article |
| id | doaj-art-28bfc0e03e00484b918e7e9eaf338d51 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-28bfc0e03e00484b918e7e9eaf338d512025-02-03T05:59:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124637137710.1155/S0161171200004336Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equationKenneth L. Jones0Xiaogui He1Yunkai Chen2Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville 28301-4298, North Carolina, USADepartment of Mathematics and Computer Science, Fayetteville State University, Fayetteville 28301-4298, North Carolina, USADepartment of Mathematics and Computer Science, Fayetteville State University, Fayetteville 28301-4298, North Carolina, USAThis paper is concerned with periodic traveling wave solutions of the forced generalized nearly concentric Korteweg-de Vries equation in the form of (uη+u/(2η)+[f(u)]ξ+uξξξ)ξ+uθθ/η2=h0. The authors first convert this equation into a forced generalized Kadomtsev-Petviashvili equation, (ut+[f(u)]x+uxxx)x+uyy=h0, and then to a nonlinear ordinary differential equation with periodic boundary conditions. An equivalent relationship between the ordinary differential equation and nonlinear integral equations with symmetric kernels is established by using the Green's function method. The integral representations generate compact operators in a Banach space of real-valued continuous functions. The Schauder's fixed point theorem is then used to prove the existence of nonconstant solutions to the integral equations. Therefore, the existence of periodic traveling wave solutions to the forced generalized KP equation, and hence the nearly concentric KdV equation, is proved.http://dx.doi.org/10.1155/S0161171200004336Existence theoremtraveling wave solution forced generalized nearly concentric Korteweg-de Vries equation. |
| spellingShingle | Kenneth L. Jones Xiaogui He Yunkai Chen Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation International Journal of Mathematics and Mathematical Sciences Existence theorem traveling wave solution forced generalized nearly concentric Korteweg-de Vries equation. |
| title | Existence of periodic traveling wave solution to the forced generalized nearly concentric
Korteweg-de Vries equation |
| title_full | Existence of periodic traveling wave solution to the forced generalized nearly concentric
Korteweg-de Vries equation |
| title_fullStr | Existence of periodic traveling wave solution to the forced generalized nearly concentric
Korteweg-de Vries equation |
| title_full_unstemmed | Existence of periodic traveling wave solution to the forced generalized nearly concentric
Korteweg-de Vries equation |
| title_short | Existence of periodic traveling wave solution to the forced generalized nearly concentric
Korteweg-de Vries equation |
| title_sort | existence of periodic traveling wave solution to the forced generalized nearly concentric korteweg de vries equation |
| topic | Existence theorem traveling wave solution forced generalized nearly concentric Korteweg-de Vries equation. |
| url | http://dx.doi.org/10.1155/S0161171200004336 |
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