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Nonlinear stability and convergence of finite-difference methods for the ”good” Boussinesq equation. (English) Zbl 0749.65082
Summary: The “good” Boussinesq equation $$u_{tt}=-u_{xxxx}+u_{xx}+(u^ 2)_{xx}$$ has recently been found to possess an interesting soliton- interaction mechanism. In this paper we study the nonlinear stability and the convergence of some simple finite-difference schemes for the numerical solution of problems involving the “good” Boussinesq equation. Numerical experiments are also reported.

##### MSC:
 65Z05 Applications to the sciences 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35Q51 Soliton equations 35L75 Higher-order nonlinear hyperbolic equations
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##### References:
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