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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200004336 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |