Pseudospectral/Delves–Freeman Computations of the Radiation Coefficient for Weakly Nonlocal Solitary Waves of the Third-Order Nonlinear Schroedinger Equation and Their Relation to Hyperasymptotic Perturbation Theory
✍ Scribed by John P. Boyd
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 646 KB
- Volume
- 138
- Category
- Article
- ISSN
- 0021-9991
No coin nor oath required. For personal study only.
✦ Synopsis
We revive a strategy of Delves to precondition a spectral calculation using an almost-diagonal Galerkin matrix. We also show that hyperasymptotic singular perturbation theory is a specialization of the Delves-Freeman iteration to a single step with a diagonal Galerkin matrix. We calculate the first three orders in the hyperasymptotic expansion of the radiation coefficient of the weakly nonlocal envelope solitary waves of the third-order nonlinear Schroedinger (TNLS) equation, which is important in fiber optics telecommunications and water waves. In a long appendix, it was necessary to develop some non-numerical but numerically essential additions to the theory of the TNLS equation: Good numerics often requires a much deeper understanding of a problem than the generation of a string of power series coefficients.