Abstract
The long-time asymptotic behavior of the solution of the Cauchy problem for the evolutionary third-order Airy equation describing wave propagation in dispersive physical media is derived by using the auxiliary parameter method. For the solution in the form of the convolution of the initial data and the Airy function, an asymptotic Erdélyi expansion in inverse powers of the cube root of the time variable with the coefficients depending on a self-similar variable and the logarithm of time is obtained. To refine the asymptotics, a family of special function classes for its coefficients is introduced. It is pointed out how the used method is connected with the geometrical optics approach and how the obtained result can be applied to nonlinear third-order PDEs.
Published Version
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