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- Title
RBF-PS Method for Eventual Periodicity Of Generalized Kawahara Equation.
- Authors
Jan, Hameed Ullah; Uddin, Marjan; Ullah, Arif; Ullah, Naseeb
- Abstract
In engineering and mathematical physics, nonlinear evolutionary equations play an important role. The Kawahara equation is one of the famous nonlinear evolution equations that appeared in the theories of shallow water waves possessing surface tension, capillary-gravity waves and also magnetoacoustic waves in a plasma. Another interesting aspect which has been observed in laboratory experiments when nonlinear evolutionary PDEs are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. This observation has been confirmed mathematically in the context of Kortewg-de-Vries (KdV) and Benjamin-Bona-Mahony (BBM) equations. In this paper we intend to show the same results hold for the generalized fifth-order Kawahara equation on bounded domain in combination with periodic boundary conditions numerically utilizing meshfree technique known as radial basis function pseudo spectral (RBF-PS) approach.
- Subjects
RADIAL basis functions; EVOLUTION equations; MATHEMATICAL physics; MESHFREE methods; PLASMA waves; NONLINEAR equations
- Publication
Applications & Applied Mathematics, 2023, Vol 18, Issue 2, p1
- ISSN
1932-9466
- Publication type
Article