Abstract
A model accounting for the influence of ice coverage on the propagation of surface sea waves is suggested. The model includes higher-order linear and nonlinear terms in the equation of wave motion. The asymptotic solution is obtained to account for nonlinear modulated wave propagation and attenuation. Two kinds of attenuation are revealed. The influence of the higher-order nonlinear, dispersion, and dissipative terms on the shape and velocity of the modulated nonlinear wave is studied. Despite the presence of higher-order terms in the original equation, the modulated solitary wave solution contains free parameters, which is important for the possible generation of such waves.
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