The concept of a space solar power station (SSPS) was proposed in 1968 as a potential
approach for solving the energy crisis. In the past 50 years, several structural concepts have …

The FORQ equation, which is bi-Hamiltonian, integrable, and hosts of a range of soliton
solutions, is viewed afresh from the viewpoint of multi-symplectic structures. A multi …

The paper provides an introduction and survey of conservative discretization methods for
Hamiltonian partial differential equations. The emphasis is on variational, symplectic and …

Numerical integration of differential equations, as an essential tool for investigating the
qualitative behaviour of the physical universe, is a very active research area since large …

Nonlinear wave equations, such as Burgers equation and compound KdV–Burgers
equation, are a class of partial differential equations (PDEs) with dissipation in Hamiltonian …

Some of the most important geometric integrators for both ordinary and partial differential
equations are reviewed and illustrated with examples in mechanics. The class of …

Two classes of efficient and robust schemes are proposed for the general multi-symplectic
Hamiltonian systems using the invariant energy quadratization (IEQ) approach. The …

Many partial differential equations (PDEs) can be written as a multi-symplectic Hamiltonian
system, which has three local conservation laws, namely multi-symplectic conservation law …

In this paper we discuss energy conservation issues related to the numerical solution of the
semilinear wave equation. As is well known, this problem can be cast as a Hamiltonian …

In this paper, we consider the multi-symplectic Runge–Kutta (MSRK) methods applied to the
nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi …