A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-
dimensional nonlinear Schrödinger equation. By establishing the equivalence between the …

We propose a family of novel, high-order numerical schemes for gradient flow models based
on the scalar auxiliary variable (SAV) approach and name them the high-order scalar …

In this paper, we develop two classes of linear high-order conservative numerical schemes
for the nonlinear Schrödinger equation with wave operator. Based on the method of order …

The numerical solutions of the two different forms of the modified Kawahara equation
namely bell-shaped soliton solutions and travelling wave solutions that occur thereby the …

When the number of nodes increases more than thousands, the arising system of global
radial basis functions (RBFs) method becomes dense and ill-conditioned. To solve this …

The focus of this paper is on the optimal error bounds of a Fourier pseudo-spectral
conservative scheme for solving the 2-dimensional nonlinear Klein–Gordon–Schrödinger …

We develop two linear, second order energy stable schemes for solving the governing
system of partial differential equations of a hydrodynamic phase field model of binary fluid …

In this paper, we present a linearly implicit energy-preserving scheme for the Camassa–
Holm equation by using the multiple scalar auxiliary variables approach, which is first …

The Kawahara equation is a model of capillary-gravity water wave and plasma waves. In this
paper, a direct method based on the Jacobi elliptic functions is presented to get analytical …

We consider two types of the generalized Korteweg–de Vries equation, where the
nonlinearity is given with or without absolute values, and, in particular, including the low …