ON NONLINEAR BIHARMONIC DISPERSIVE WAVE EQUATIONS (FUDMA JOURNAL OF SCIENCES, 2025)
This paper proposes and studies particular nonlinear dispersive biharmonic equation, whose related equations appear in various physical phenomena such as wave propagation in nonlinear media and plasma physics. We chose the power kind of nonlinearity as it is common in these areas. We show that the linear version exhibits strong dispersive behaviour while the nonlinear version reveals possible emergence of singularities for higher degree nonlinearity exponent . Both versions of the equation, linear and nonlinear, were solved analytically where for the latter we use perturbation approach and Fourier transform for the former. A glimpse towards the symmetry analysis of the underlying equations is provided and somewhat insights into the behaviour of the solution is discussed.
Keywords: Biharmonic; dispersion; nonlinearities; singularities; perturbation; numerics