A system of coupled partial differential equations exhibiting both elevation and depression rogue wave modes. (September 2015)

• Record Type: Journal Article
• Authors: Wu, C.F.; Chan, H.N.; Chow, K.W.
• Is Part Of: Applied mathematics letters. Volume 47(2015:Sep.)
• Page Start: 35
• Page End: 42
• Publication Date: 2015-09
• Subjects: Breathers -- Algebraic solitons -- Rogue waves; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.02.021
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Analytical solutions are obtained for a coupled system of partial differential equations involving hyperbolic differential operators. Oscillatory states are calculated by the Hirota bilinear transformation. Algebraically localized modes are derived by taking a Taylor expansion. Physically these equations will model the dynamics of water waves, where the dependent variable (typically the displacement of the free surface) can exhibit a sudden deviation from an otherwise tranquil background. Such modes are termed 'rogue waves' and are associated with 'extreme and rare events in physics'. Furthermore, elevations, depressions and 'four-petal' rogue waves can all be obtained by modifying the input parameters.