Nonlinear Wave Equation in Special Coordinates

Nonlinear Wave Equation in Special Coordinates

Some classical types of nonlinear periodic wave motion are studied in special coordinates. In the case of cylinder coordinates, the usual perturbation techniques leads to the overdetermined systems of linear algebraic equations for unknown coefficients whose compatibility is key step of the investigation. Their solutions give solutions to the nonlinear wave equation which are periodic in time a...

Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates

Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time t, the Hankel transform with respect to the radial coordinate r, the finite Fourier transform with respect to the angular coordinate φ, and the exponential Fourier transfor...

Forced Vibrations for a Nonlinear Wave Equation

Nonlinear wave evolution equation for critical layers.

Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solut...

Nonlinear progressive wave equation for stratified atmospheres.

The nonlinear progressive wave equation (NPE) [McDonald and Kuperman, J. Acoust. Soc. Am. 81, 1406-1417 (1987)] is expressed in a form to accommodate changes in the ambient atmospheric density, pressure, and sound speed as the time-stepping computational window moves along a path possibly traversing significant altitude differences (in pressure scale heights). The modification is accomplished b...