Abstract
We consider a fifth-order KdV equation, where the fifth-order derivative term is multiplied by a small parameter. It has been conjectured that this equation admits a non-local solitary wave solution which has a central core and an oscillatory tail either behind or in front of the core. We prove that this solution cannot be exactly steady, and instead the amplitude of the central core decays due to the energy flux generated in the oscillatory tail. The decay rate is calculated in the limit as the parameter tends to zero. In order to verify the analytical results, we have developed a high-precision spectral method for numerical integration of this equation. The analytical and numerical result show good agreement.
Original language | English |
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Pages (from-to) | 270-278 |
Number of pages | 9 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 69 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 15 Dec 1993 |
Externally published | Yes |