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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 414060, 26 pages
Research Article

-Advanced Models for Tsunami and Rogue Waves

Department of Mathematics, East Carolina University, Greenville, NC 27858, USA

Received 9 March 2012; Revised 19 May 2012; Accepted 21 May 2012

Academic Editor: Ferhan M. Atici

Copyright © 2012 D. W. Pravica et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A wavelet , that satisfies the q-advanced differential equation for , is used to model N-wave oscillations observed in tsunamis. Although q-advanced ODEs may seem nonphysical, we present an application that model tsunamis, in particular the Japanese tsunami of March 11, 2011, by utilizing a one-dimensional wave equation that is forced by . The profile is similar to tsunami models in present use. The function is a wavelet that satisfies a q-advanced harmonic oscillator equation. It is also shown that another wavelet, , matches a rogue-wave profile. This is explained in terms of a resonance wherein two small amplitude forcing waves eventually lead to a large amplitude rogue. Since wavelets are used in the detection of tsunamis and rogues, the signal-analysis performance of and is examined on actual data.