University of Limerick, Ireland
eugene.benilov@ul.ie
Solitary and Periodic Waves in a Fifth-Order Korteweg-de Vries Equation
Thursday, 23 March 2023 at 15:00
On line: http://meet.google.com/nif-zfwd-mrg
Abstract
I consider a fifth-order KdV equation, where the fifth-order derivative term is multiplied by a small parameter ε. 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. I shall prove that this solution cannot be exactly steady; 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 ε → 0. In order to verify the analytical results, I have developed a high-precision spectral method for numerical integration of this equation. The asymptotic and numerical result show good agreement.
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