2013/09/23 by Nathan Totz, Totz, Nathan · 2 citations
Computer Science · Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Arctic and Antarctic ice dynamics #FOS: Mathematics #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1309.5995
openalex publication_date 2013/09/23 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We consider small amplitude wave packet-like solutions to the 3D inviscid\nincompressible irrotational infinite depth water wave problem neglecting\nsurface tension. Formal multiscale calculations suggest that the modulation of\nsuch a solution is described by a profile traveling at group velocity and\ngoverned by a hyperbolic cubic nonlinear Schr "odinger equation. In this paper\nwe show that, given wave packet initial data, the corresponding solution exists\nand retains the form of a wave packet on natural NLS time scales. Moreover, we\ngive rigorous error estimates between the true and formal solutions on the\nappropriate time scale in Sobolev spaces using the energy method. The proof\nproceeds by directly applying modulational analysis to the formulation of the\n3D water wave problem developed by Sijue Wu.\n