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- W2051923885 abstract "The paper studies the influence of the time discretizations when simulating some phenomena involving more than one solitary wave. Taking the KdV equation as a case study, we obtain some conditions on the numerical method in order to get a more correct simulation of multi-soliton solutions. They are related to the evolution of the conserved quantities of the problem through the numerical integration. It is shown that, when approximating N-solitons, a method that preserves N invariants of the problem shows a better time propagation of the error than that of a general scheme. As a consequence of this, the simulation of some physical parameters that characterize the waves is more suitable when using conservative integrators. We also show how these results can be extended to the approximation to multi-solitons of any equation of the KdV hierarchy and, more generally, other integrable equations." @default.
- W2051923885 created "2016-06-24" @default.
- W2051923885 creator A5042635297 @default.
- W2051923885 creator A5046552014 @default.
- W2051923885 date "2010-10-01" @default.
- W2051923885 modified "2023-09-23" @default.
- W2051923885 title "Error propagation when approximating multi-solitons: The KdV equation as a case study" @default.
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- W2051923885 doi "https://doi.org/10.1016/j.amc.2009.06.033" @default.
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