Multi-pulse solitary waves in a fourth-order nonlinear Schrödinger equation

Abstract

In the present work, we consider the existence and spectral stability of multi-pulse solitary wave solutions to a nonlinear Schrödinger equation with both fourth and second order dispersion terms. We first give a criterion for the existence of a single solitary wave solution in terms of the coefficients of the dispersion terms, and then show that a discrete family of multi-pulse solutions exists which is characterized by the distances between the individual pulses. We then reduce the spectral stability problem for these multi-pulses to computing the determinant of a matrix which is, to leading order, block diagonal. Under an additional assumption, which can be verified numerically, we show that all multi-pulses are spectrally unstable. For double pulses, numerical computations are presented which are in good agreement with our analytical results.

arXiv comment22 pages, 10 figures

References in corpus (3)

• Pure-Quartic Solitons
• Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems
• A reformulated Krein matrix for star-even polynomial operators with applications

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