Memories of Hirota's method: Application to the reduced Maxwell-Bloch system in the early 1970s

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 369, Issue 1939, 2011, Pages 1215-1227

  Caudrey, P J ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Non linear partial differential equations; Nonlinear optics; Solitons

Indexed keywords

NONLINEAR OPTICS; OPTICAL MATERIALS; PARTIAL DIFFERENTIAL EQUATIONS; SCATTERING; SOLITONS;

BILINEAR FORM; DIRECT METHOD; INVERSE SCATTERING METHODS; KORTEWEG-DE VRIES EQUATIONS; MAXWELL-BLOCH SYSTEM; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 79953225503     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2010.0337     Document Type: Article

References (6)

1. Gardner, C. S., Greene, J. M., Kruskal, M. D. & Miura, R. M. 1967 Method for solving the KdV equation. Phys. Rev. Lett. 19, 1095-1097. (doi:10.1103/PhysRevLett.19.1095)
2. Hirota, R. 1971 Exact solution of the KdV equation for multiple collision of solitons. Phys. Rev. Lett. 27, 1192-1194. (doi:10.1103/PhysRevLett.27.1192)
3. Hirota, R. 1972 Exact solution of the sine-Gordon equation for multiple collision of solitons. J. Phys. Soc. Jpn 33, 1459-1463. (doi:10.1143/JPSJ.33. 1459)
4. Caudrey, P. J., Eilbeck, J. C., Gibbon, J. D. & Bullough, R. K. 1973 Multiple soliton and bisoliton bound state solutions of the sine-Gordon equation and related equations in nonlinear optics. J. Phys. A: Math. Nucl. Gen. 6, L112-L115. (doi:10.1088/0305-4470/6/8/002)
5. Hirota, R. 1980 Direct methods in soliton theory. In Solitons (eds R. K. Bullough & P. J. Caudrey), pp. 157-176. Berlin, Germany: Springer.
6. Caudrey, P. J., Eilbeck, J. C. & Gibbon, J. D. 1974 Exact multisoliton solution of the reduced Maxwell-Bloch equations of nonlinear optics. J. Appl. Math. 14, 375-386.