Solitons Of Whitham Equation With Resonance Dispersion

Localized stationary solutions of nonlinear nonlocal Whitham equation with resonance dispersion relation are considered. The existence of exponentially localized smooth and singular solitons, bound states of the solitons and localized solutions with oscillating asymptotics is recognized. The velocity spectra of solitons, in contrast to all other known Whitham equations, appear to be discrete. Asymptotic "quantization rules" for calculation of discrete spectra are obtained.(c) 2020 Elsevier Ltd. All rights reserved.