Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media
In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J.…
Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory
In the present script, a four-parameter family of Boussinesq systems are derived from the two-dimensional Euler equations for free-surface flow and criteria are formulated to help decide which of these equations one might choose in a given modeling situation.
Exact Traveling-Wave Solutions to Bidirectional Wave Equations
- Min Chen
- Mathematics
- 1 May 1998
AbstractIn this paper, we present several systematicways to find exact traveling-wave solutions of thesystems
$$\eta _t + u_x + \left( {u\eta } \right)_x + au_{xxx} - b\eta _{xxt} = 0$$
$$u_t + \eta…
Exact solutions of various Boussinesq systems
- Min Chen
- Mathematics
- 1 September 1998
Solitary-wave and multi-pulsed traveling-wave solutions of boussinesq systems
- Min Chen
- Mathematics
- 1 June 2000
This paper studies traveling-wave solutions of the partial differential equations which model waves in a horizontal water channel traveling in both directions. The existence of solitary-wave…
Cnoidal wave solutions to Boussinesq systems
- Hongqiu Chen, Min Chen, Nghiem Nguyen
- Mathematics
- 1 June 2007
In this paper, two different techniques will be employed to study the cnoidal wave solutions of the Boussinesq systems. First, the existence of periodic travelling-wave solutions for a large family…
Singular Solutions of a Boussinesq System for Water Waves
Studied here is the Boussinesq system ηt+ux+(ηu)x+auxxx−bηxxt=0, ut+ηx+ 1 2 (u)x+cηxxx−duxxt=0, of partial differential equations. This system has been used in theory and practice as a model for…
Comparisons between the BBM equation and a Boussinesq system
- A. Alazman, J. Albert, J. Bona, Min Chen, J. Wu
- MathematicsAdvances in Differential Equations
- 1 January 2006
This project aims to cast light on a Boussinesq system of equations modelling two-way propagation of surface waves. Included in the study are existence results, comparisons between the Boussinesq…
Long-time asymptotic behavior of two-dimensional dissipativeBoussinesq systems
In this article, we consider the two-dimensional
dissipative Boussinesq systems which model surface waves in three
space dimensions. The long time asymptotics of the solutions for a
large class…
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