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- W4301719105 abstract "We will discuss an extension of the pseudospectral method developed by Wineberg, McGrath, Gabl, and Scott for the numerical integration of the KdV initial value problem. Our generalization of their algorithm can be used to solve initial value problems for a wide class of evolution equations that are weakly nonlinear in a sense that we will make precise. This class includes in particular the other classical soliton equations (SGE and NLS). As well as being very simple to implement, this method exhibits remarkable speed and stability, making it ideal for use with visualization tools where it makes it possible to experiment in real-time with soliton interactions and to see how a general solution decomposes into solitons. We will analyze the structure of the algorithm, discuss some of the reasons behind its robust numerical behavior, and finally describe a fixed point theorem we have found that proves that the pseudospectral stepping algorithm converges." @default.
- W4301719105 created "2022-10-05" @default.
- W4301719105 creator A5057918239 @default.
- W4301719105 date "2014-09-10" @default.
- W4301719105 modified "2023-10-18" @default.
- W4301719105 title "The Initial Value Problem for Weakly Nonlinear PDE" @default.
- W4301719105 doi "https://doi.org/10.48550/arxiv.1409.3214" @default.
- W4301719105 hasPublicationYear "2014" @default.
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