Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime

Deniz Bilman, University of Cincinnati, Ohio, and Peter D. Miller, University of Michigan, Ann Arbor, Michigan

1. Introduction 2. Far-field asymptotic behavior in the domain $\mathcal {C}$ 3. Properties of $h(\lambda ;\chi ,\tau )$ for $(\chi ,\tau )\in \mathcal {E}\cup \mathcal {S}$ 4. Far-Field Asymptotic Behavior of Rogue Waves in the Domain $\mathcal {E}$ 5. Far-Field Asymptotic Behavior in the Domain $\mathcal {S}$ A. Relative Perturbations of Plane Waves and Linear Instability Bands B. Proofs of Some Elementary Results C. Some Useful Facts About Polynomials with Real Coefficients