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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.Expand
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. Expand
A Boussinesq system for two-way propagation of nonlinear dispersive waves
Abstract In this report, we study the system N t + W x + (NW) x − 1 6 N xxt = 0 , W t + N x + WW x − 1 6 W xxt = 0 , (∗) which describes approximately the two-dimensional propagation of surface wavesExpand
Exact Traveling-Wave Solutions to Bidirectional Wave Equations
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 + \etaExpand
Nonlinear Galerkin method in the finite difference case and wavelet-like incremental unknowns
SummaryThe IMG algorithm (Inertial Manifold-Multigrid algorithm) which uses the first-order incremental unknowns was introduced in [20]. The IMG algorithm is aimed at numerically implementingExpand
Exact solutions of various Boussinesq systems
Abstract It was shown in [1,2] that surface water waves in a water tunnel can be described by systems of the form η t +u x +(uη) x +au xxx −bη xxt =0, u t +η x +uu x +cη xxx −du xxt =0 , where a, b,Expand
Discreteness and Convergence of Möbius Groups
In this paper we show that one can use a fixed nontrivial Möbius transformation as a test map to test the discreteness of a nonelementary Möbius group. We also establish two theorems in algebraicExpand
Solitary-wave and multi-pulsed traveling-wave solutions of boussinesq systems
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-waveExpand
Incremental unknowns for solving partial differential equations
SummaryIncremental unknowns have been proposed in [T] as a method to approximate fractal attractors by using finite difference approximations of evolution equations. In the case of linear ellipticExpand
Incremental unknowns in finite differences: condition number of the matrix
The utilization of incremental unknowns (IU) with multilevel finite differences was proposed in [R. Temam, SIAM J. Math. Anal., 21 (1991), pp. 154–178] for the integration of elliptic partialExpand