Traveling wave solutions of the nonlinear Gilson-Pickering equation in crystal lattice theory

This paper focuses on obtaining the traveling wave solutions of the nonlinear Gilson-Pickering equa-tion(GPE),which describes the prorogation of waves in crystal lattice theory and plasma physics.The solution of the GPE is approximated via the finite difference technique and the localized meshless radial basis function generated finite difference.The association of the technique results in a meshless approach that does not require linearizing the nonlinear terms.At the first step,the PDE is converted to a system of nonlinear ODEs with the help of the radial kernels.In the second step,a high-order ODE solver is adopted to discretize the nonlinear ODE system.The global collocation techniques pose a considerable computationl burden due to the calculation of the dense algebraic system.The proposed method approx-imates differential operators over the local support domain,leading to sparse differentiation matrices and decreasing the computational burden.Numerical results and comparisons are provided to confirm the efficiency and accuracy of the method.

Solution for generalized fuzzy fractional Kortewege-de Varies equation using a robust fuzzy double parametric approach

The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a crystal lattice.This paper focuses on developing and analysing a resilient double parametric analytical approach for the nonlinear fuzzy fractional KdV equation(FFKdVE)under gH-differentiability of Caputo fractional order,namely the q-Homotopy analysis method with the Shehu transform(q-HASTM).A triangular fuzzy number describes the Caputo fractional derivative of orderα,0<α≤1,for modelling problem.The fuzzy velocity profiles with crisp and fuzzy conditions at different spatial positions are in-vestigated using a robust double parametric form-based q-HASTM with its convergence analysis.The ob-tained results are compared with existing works in the literature to confirm the efficacy and effectiveness of the method.

Bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals

This study focuses on the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically,and numerically.The analytical results are obtained using thenormal form technique and numerical results are obtained using the numerical continuation method.For this model,a number of bifurcations are studied,including the transcritical(pitchfork)and fip bifurcations,the Neimark-Sacker(NS)bifurcations,and the strong resonance bifurcations.We especially determine the dynamical behaviors of the model for higher iterations up to fourth-order.Numerical simulation is employed to present a closed invariant curve emerging about an NS point,and its breaking down to several closed invariant curves and eventuality giving rise to a chaotic strange attractor by increasing the bifurcation parameter.

Numerical treatment of temporal-fractional porous medium model occurring in fractured media

This paper proposes a temporal-fractional porous medium model(T-FPMM)for describing the co-current and counter-current imbibition,which arises in a water-wet fractured porous media.The correlation be-tween the co-current and counter-current imbibition for the fractures and porous matrix are examined to determine the saturation and recovery rate of the reservoir.For different fractional orders in both porous matrix and fractured porous media,the homotopy analysis technique and its stability analysis are used to explore the parametric behavior of the saturation and recovery rates.Finally,the effects of wettability and inclination on the recovery rate and saturation are studied for distinct fractional values.