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- W934421831 abstract "This chapter presents the numerical methods for computing the Riemann spectrum by loop integrals methods; in particular, the results for the Korteweg-de Vries (KdV) equation are given. The chapter describes the computation of the generic loop integral Gij and how to remove singularities from the numerical computations due to particular configurations of the inverse scattering transform (IST) eigenvalues. Two kinds of singularities (or near singularities) exist in the loop integrals. The first occurs exactly at the band edges, and these are trivially accounted for. The second is a near singularity that occurs in the nearest eigenvalues immediately to the right and left of the band-edge integration limits. The near singularities occur either in the small-amplitude limit (for sine waves, the near-degenerate case occurs when two open-band eigenvalues are nearly equal) or in the large-amplitude soliton limit (when two adjacent gap eigenvalues are nearly equal). The chapter discusses the procedure for convenient transformations that includes first transformation, second transformation, and a final transformation. The chapter also describes the arithmetic-geometric mean (AGM) method for the loop integrals." @default.
- W934421831 created "2016-06-24" @default.
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- W934421831 date "2010-01-01" @default.
- W934421831 modified "2023-09-24" @default.
- W934421831 title "Computation of Algebraic-Geometric Loop Integrals for the KdV Equation" @default.
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- W934421831 doi "https://doi.org/10.1016/s0074-6142(10)97019-8" @default.
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