Integrability and self-similarity in transient stimulated Raman scattering

DOI10.1007/s003329900062zbMath0959.78008OpenAlexW2050903630MaRDI QIDQ1277226

Athanassios S. Fokas, Curtis R. Menyuk

Publication date: 11 April 1999

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s003329900062

zbMATH Keywords

self-similar solutionasymptotic analysislinear integral equationLax pairRiemann-Hilbert problemsintegrable equationsinverse spectral methodinitial-boundary valuelong-distance behaviormaterial excitationpump electric fieldRaman cellsimulated Raman scatteringStokes electric fieldthird Painlevé transcendenttransient limit

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Diffraction, scattering (78A45) Fredholm integral equations (45B05) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Asymptotic analysis in optics and electromagnetic theory (78M35)

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