Existence and stability of standing waves for nonlinear fractional Schrödinger equations J. Math. Phys. 53, 083702 (2012) N-fold Darboux transformations and soliton solutions of three nonlinear equations J. Math. Phys. 53, 083502 (2012) Some algebro-geometric solutions for the coupled modified Kadomtsev-Petviashvili equations arising from the Neumann type systems

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Two different linearized schemes are applied to a parametric finite-difference scheme concerning the numerical solution of the Boussinesq equation. At the first linearized scheme the nonlinear term of the equation is substituted by an appropriate value, while at the second scheme we use Taylor's expansion. Both schemes are analyzed for local truncation error, stability and convergence. The results of the experiments are examined for their accuracy for the single and the double-soliton waves to known from the bibliography numerical schemes.

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