The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable
models, is a method for solving integrable partial differential equations governing wave …

In this paper, numerical methods are suggested to compute the discrete and the continuous
spectrum of a signal with respect to the Zakharov-Shabat system, a Lax operator underlying …

We present a new numerical scheme for nonlinear Schrödinger type equations. The scheme
conserves the energy and charge of the systems and it is linearly implicit. Numerical …

We investigate the self-trapping phenomenon in one-dimensional nonlinear waveguide
arrays. We discuss various approximate analytical descriptions of the discrete self-trapped …

Resonances are ubiquitous in dynamical systems with many degrees of freedom. They have
the basic effect of introducing slow-fast behavior in an evolutionary system which, coupled …

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 …

Numerical integration schemes for coupled time-dependent nonlinear Schrodinger
equations are examined using exponential splitting step methods. Exponentiation of the …

Surface wave data from the Adriatic Sea are analysed in the light of new data analysis
techniques which may be viewed as a nonlinear generalization of the ordinary Fourier …

Many studies have shown that nonintegrable systems with modulational instabilities
constrained by more than one conservation law exhibit universal long time behavior …

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