Numerical modeling of the ion-acoustic solitary waves arising in nonlinear dispersive system

This paper proposes a numerical scheme for the (2 + 1)-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation (ZK-BBME). The ZK-BBME represents a long-wave model with large wavelength that explains the water wave phenomena in nonlinear dispersive system. The solution of the ZK-BBME is discretized by using hybridization of the finite difference and localized radial basis function based on partition of unity method. The association of this hybridization leads to a meshless method and it does not requires any linearization. In the initial step, the PDE is converted into a nonlinear ODE system by making use of radial kernels. In the next step, the obtained nonlinear ODE system is solved based on an ODE solver of high order. The global collocation technique imposes a large computational cost because a dense algebraic system must be calculated. This proposed strategy is based on decomposing the initial domain into a number of sub-domains using kernel approximation on each sub-domain. Three numerical examples are illustrated to clarify the efficiency and accuracy of the proposed strategy.