ON NONLINEAR BIHARMONIC DISPERSIVE WAVE EQUATIONS

Sadiq Shehu Sabo; Umar Muhammad Dauda; Sunday Babuba; Abba Ibrahim Bakari

doi:10.33003/fjs-2025-0901-2925

Sadiq Shehu Sabo Department of Mathematics, Faculty of Science, Federal University, Dutse, Jigawa State
Umar Muhammad Dauda Aliko Dangote University of Science & Technology, Wudil
Sunday Babuba Department of Mathematics, Faculty of Science, Federal University, Dutse, Jigawa State
Abba Ibrahim Bakari Department of Mathematics, Faculty of Science, Federal University, Dutse, Jigawa State

DOI: https://doi.org/10.33003/fjs-2025-0901-2925

Keywords: Biharmonic, dispersion, nonlinearities, singularities, perturbation, numerics

Abstract

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.

Author Biography

Sadiq Shehu Sabo, Department of Mathematics, Faculty of Science, Federal University, Dutse, Jigawa State

An MSc Student.

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ON NONLINEAR BIHARMONIC DISPERSIVE WAVE EQUATIONS

Abstract

Author Biography

References

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