Efficient numerical algorithms for the solution of “good” Boussinesq equation in water wave propagation

Spectrally accurate energy‐preserving methods for the numerical solution of the “good” Boussinesq equation

“…commonly used to describe small amplitude long waves propagation on the surface of shallow water. It is for this reason that the equation is often considered in several physical contexts, such as ocean and coastal engineering (as stressed, e.g., in [1,2]). Moreover, the equation provides a balance between dispersion and nonlinearity that may lead to either the existence of solitons, or blowup solutions [3][4][5][6][7][8][9].…”

Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients

“…The schemes possess good numerical stability. Compact schemes are popular recently due to high accuracy, compactness, and economic resource in scientific computation [15][16][17]. In this paper, applying compact operators, we construct symplectic methods to the initial boundary problems of the linear Schrödinger equation with a variable coefficient and a stochastic perturbation term (denoted by LSES):…”

Nonlinear Fractional Jaulent-Miodek and Whitham-Broer-Kaup Equations within Sumudu Transform

“…FWBK equation (1) describes the dispersive long wave in shallow water, where ( , ) is the field of horizontal velocity, V( , ) is the height which deviates from the equilibrium position of liquid, and and are constants that represent different powers. If = 0 and = 1, (1) reduces to the classical long-wave equations which describe the shallow water wave with diffusion [6]. If = 1 and = 0, (1) becomes the modified Boussinesq equations [7,8].…”