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korteweg–de vries equation with delay

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Periodic and solitary waves in a Korteweg–de Vries equation with delay
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Qi Qiao, Shuling Yan, Xiang Zhang
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View

Published online by Cambridge University Press:

07 September 2023, pp. 1-23
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For a perturbed generalized Korteweg–de Vries equation with a distributed delay, we prove the existence of both periodic and solitary waves by using the geometric singular perturbation theory and the Melnikov method. We further obtain monotonicity and boundedness of the speed of the periodic wave with respect to the total energy of the unperturbed system. Finally, we establish a relation between the wave speed and the wavelength.