Weakly non-local solitary wave solutions 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]. This equation describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 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. Using 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, 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.

authors

• Daripa, Prabir

published proceedings

• Mathematics and Computers in Simulation

author list (cited authors)

• Daripa, P., & Dash, R. K.

complete list of authors

• Daripa, Prabir||Dash, Ranjan K

publication date

• January 2001

publisher

• Elsevier  Publisher

published in

• Mathematics and Computers in Simulation  Journal

keywords

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

start page

• 393

end page

• 405

volume

• 55

issue

• 4