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A robust semi-explicit difference scheme for the Kuramoto-Tsuzuki equation. (English) Zbl 1181.65117
The paper deals with the Kuramoto-Tsuzuki equation $$\frac{\partial w}{\partial t}=(1+ic_1)\frac{\partial^2 w}{\partial x^2}+w-(1+ic_2)|w|^2w, \; (x,t)\in (0,1) \times (0,T]$$ with an initial condition and with the homogeneous Neumann boundary conditions. The authors propose an semi-explicit linearized difference scheme of Crank-Nicolson type with the truncation error ${\mathcal O}(h^2+\tau^2).$ It is proved that the scheme is stable and possesses the accuracy order ${\mathcal O}(h^2+\tau^2)$ in the $L_{\infty}$-norm. Numerical examples confirm the theoretical results.

##### MSC:
 65M06 Finite difference methods (IVP of PDE) 65M12 Stability and convergence of numerical methods (IVP of PDE) 65M15 Error bounds (IVP of PDE) 35Q53 KdV-like (Korteweg-de Vries) equations
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##### References:
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