Analytical and numerical studies of a singularly perturbed Boussinesq equation Academic Article

abstract

• We study the singularly perturbed (sixth-order) Boussinesq equation recently introduced by Daripa and Hua [Appl. Math. Comput. 101 (1999) 159]. Motivated by their work, we formally derive this equation from two-dimensional potential flow equations governing the small amplitude long capillary-gravity waves on the surface of shallow water for Bond number very close to but less than 1/3. On the basis of far-field analyses and heuristic arguments, we show that the traveling wave solutions of this equation are weakly non-local solitary waves characterized by small amplitude fast oscillations in the far-field. We review various analytical and numerical methods originally devised to obtain this type of weakly non-local solitary wave solutions of the singularly perturbed (fifth-order) KdV equation. Using these methods, we obtain weakly non-local solitary wave solutions of the singularly perturbed (sixth-order) Boussinesq equation and provide estimates of the amplitude of oscillations which persist in the far-field. 2002 Elsevier Science Inc. All rights reserved.

authors

• Daripa, Prabir

published proceedings

• APPLIED MATHEMATICS AND COMPUTATION

author list (cited authors)

• Dash, R. K., & Daripa, P.

citation count

• 18

complete list of authors

• Dash, RK||Daripa, P

publication date

• February 2002

publisher

• Elsevier  Publisher

keywords

• Asymptotics Beyond All Orders
• Capillary-gravity Waves
• Pseudospectral Method
• Singularly Perturbed Boussinesq Equation
• Weakly Non-local Solitary Waves

Digital Object Identifier (DOI)

• 10.1016/S0096-3003(01)00166-7

start page

• 1

end page

• 30

volume

• 126

issue

• 1

URL

• http://dx.doi.org/10.1016/s0096-3003(01)00166-7