Higher-Order Hamiltonian Model for Unidirectional Water Waves

Author(s)

Bona, J. L. ^[1] ; Carvajal, X. ^[2] ; Panthee, M. ^[3] ; Scialom, M. ^[3]

Affiliation

^[1] Univ Illinois, Dept Math Stat & Comp Sci, 851 S Morgan St MC 249, Chicago, IL 60607 - USA

^[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941909 Rio De Janeiro, RJ - Brazil

^[3] Univ Estadual Campinas, IMECC, BR-13083859 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF NONLINEAR SCIENCE; v. 28, n. 2, p. 543-577, APR 2018.
• Web of Science Citations: 2

Abstract

Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer timescale. The initial value problem for the class of equations that emerges from our derivation is then considered. A local well-posedness theory is straightforwardly established by a contraction mapping argument. A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely. (AU)

• FAPESP's process: 16/01544-2 - Higher order models for waves in nonlinear, dispersive media
• Grantee: Marcia Assumpcao Guimaraes Scialom
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 16/25864-6 - Nonlinear Evolution Equations of Dispersive Type
• Grantee: Mahendra Prasad Panthee
• Support Opportunities: Regular Research Grants
• FAPESP's process: 12/23054-6 - Properties of solutions of some dispersive equations
• Grantee: Marcia Assumpcao Guimaraes Scialom
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil