A generalized Sasa–Satsuma equation on the line is studied via the Riemann–Hilbert
approach. Firstly we derive a Lax pair associated with a 3× 3 matrix spectral problem for the …

This book grew out of the collaboration of the authors, which began in the Spring of 2010,
and the first author's PhD dissertation. The second author developed much of the theory in …

We study the fundamental rogue wave solutions of the focusing nonlinear Schrödinger
equation in the limit of large order. Using a recently proposed Riemann–Hilbert …

Using the resolvent operator, we develop an algorithm for computing smoothed
approximations of spectral measures associated with self-adjoint operators. The algorithm …

Spectral measures arise in numerous applications such as quantum mechanics, signal
processing, resonance phenomena, and fluid stability analysis. Similarly, spectral …

The Foundations of Infinite-Dimensional Spectral Computations Page 1 The Foundations of
Infinite-Dimensional Spectral Computations Matthew J. Colbrook St John’s College University …

We consider the model of the focusing one-dimensional nonlinear Schrödinger equation
(fNLSE) in the presence of an unstable constant background, which exhibits coherent …

In this paper, we develop the numerical inverse scattering transform (NIST) for the focusing
and defocusing Kundu–Eckhaus (KE) equations. The NIST consists of numerical direct …

Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant
but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through …

We solve the focusing and defocusing nonlinear Schrödinger (NLS) equations numerically
by implementing the inverse scattering transform. The computation of the scattering data and …