Water wave propagation phenomena still attract the interest of researchers from many areas and with various objectives. The dispersive equations, including a large body of classes, are widely used models for a great number of problems in the fields of physics, chemistry and biology. For instance, the Korteweg-de Vries (KdV) equation is one of the famous dispersive wave equation appeared in the theories of shallow water waves with the assumption of small wave-amplitude and large wave length, also its various modifications serve as the modeling equations in several physical problems. Another interesting qualitative characteristic of solutions of some dispersive wave equations indicated through experiments that are connected with their large-time behavior termed as Eventual Time Periodicity which is exhibited by solutions of initial-boundary-value problems (IBVPs henceforth). Laboratory experiments in a channel with a flap-type or piston-type wave maker mounted at one end of a channel exposed this interesting phenomena. Here in this study we numerically investigate the solutions periodicity for linearized KdV type equations on a finite (bounded) domain with periodic boundary conditions using meshfree technique known as Radial basis function pseudo spectral (RBF-PS) method.
Jan, Hameed Ullah; Uddin, Marjan; Norin, Asma; and ., Tamheeda
(R1969) On the Approximation of Eventual Periodicity of Linearized KdV Type Equations using RBF-PS Method,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
2, Article 16.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss2/16