In recent years, the numerical solution of differential problems, possessing constants of
motion, has been attacked by imposing the vanishing of a corresponding line integral. The …

In recent years, the efficient numerical solution of Hamiltonian problems has led to the
definition of a class of energy-conserving Runge–Kutta methods named Hamiltonian …

A novel class of high-order linearly implicit energy-preserving integrating factor Runge–
Kutta methods are proposed for the nonlinear Schrödinger equation. Based on the idea of …

In this paper, we reformulate the coupled nonlinear Schrödinger (CNLS) equation by using
the scalar auxiliary variable (SAV) approach and solve the resulting system by using Crank …

In this paper, we study the efficient solution of the nonlinear Schrödinger equation with wave
operator, subject to periodic boundary conditions. In such a case, it is known that its solution …

In this paper, we present a fully discrete and structure-preserving scheme for the nonlinear
fractional Schrödinger equations. The key is to introduce a scalar auxiliary variable and …

In this paper, a family of arbitrarily high-order structure-preserving exponential Runge–Kutta
methods are developed for the nonlinear Schrödinger equation by combining the scalar …

Recently, the numerical solution of multi-frequency, highly oscillatory Hamiltonian problems
has been attacked by using Hamiltonian boundary value methods (HBVMs) as spectral …

Multi-frequency, highly oscillatory Hamiltonian problems derive from the mathematical
modelling of many real-life applications. We here propose a variant of Hamiltonian …

Recently, the numerical solution of stiffly/highly oscillatory Hamiltonian problems has been
attacked by using Hamiltonian boundary value methods (HBVMs) as spectral methods in …