Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the
description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be …

An efficient numerical method for solution of nonlinear evolution equations based on the
Haar wavelets approach is proposed. The method is tested in the case of Burgers and sine …

In this paper, we develop a novel, linearly implicit and local energy-preserving scheme for
the sine-Gordon equation. The basic idea is from the invariant energy quadratization …

This paper explores the utility of a discrete singular convolution (DSC) algorithm for the
integration of the sine-Gordon equation. The initial values are chosen close to a homoclinic …

We propose two general finite-difference schemes that inherit energy conservation property
from nonlinear wave equations, such as the nonlinear Klein–Gordon equation (NLKGE) …

In this work we propose a high-order and accurate method for solving the one-dimensional
nonlinear sine–Gordon equation. The proposed method is based on applying a compact …

The decomposition method for solving the sine-Gordon equation has been implemented. By
using a number of initial values, the explicit and numerical solutions of the equation are …

Recently an interesting new class of PDE integrators, multisymplectic schemes, has been
introduced for solving systems possessing a certain multisymplectic structure. Some of the …

Based on the Darboux–Bäcklund transformation, we construct the exact solutions and their
derivatives expressed in theta functions under the backgrounds of the librational and …

The term'optimization'refers to the process of maximizing the beneficial attributes of a
mathematical function or system while minimizing the unfavorable ones. The majority of real …