zbMATH — the first resource for mathematics

Reduction of soliton equations in bilinear form. (English) Zbl 0601.35099
The author generalizes the studies of the Kyoto group (M. Sato, Y. Sato, E. Date, M. Kashivara, M. Jimbo, T. Miva) on the reduction of the Kadomtsev-Petviashvili equation (KP) to the Korteweg de Vries equation (KdV), the Boussinesq equation and on some other reductions. The paper introduces a so called ”n-pseudo reduction” method and a special reduction \((pq=c)\) which being applied to the KP hierarchy generates the classical Boussinesq equation and nonlinear Schrödinger equation exhibiting Dark-soliton solutions. A reduction of the Boussinesq-KP equation generates the \(''KdV+Sawada\)-Kotera” equation which exhibits resonances of solitons.
Reviewer: J.Kostarčuk

35Q99 Partial differential equations of mathematical physics and other areas of application
Full Text: DOI
[1] Jimbo, Michio; Miwa, Tetsuji, Solitons and infinite dimensional Lie algebras, Publ. RIMS, Kyoto univ., 19, 943, (1983) · Zbl 0557.35091
[2] Satsuma, Junkichi; Hirota, Ryogo, J. phys. soc. jpn., 51, 3390, (1982)
[3] Hirota, Ryogo; Satsuma, Junkichi, Progr. theor. phys., 57, 797, (1977)
[4] Hirota, Ryogo, Classical Boussinesq equation is a reduction of the modified KP equation, J. phys. soc. jpn., 54, 2409, (1985)
[5] Hirota, Ryogo; Ito, Masaaki, J. phys. soc. jpn., 52, 744, (1983)
[6] Hirota, Ryogo, Direct method in soliton theory, () · Zbl 1099.35111
[7] Lax, P.D., Comm. pure and appl. math., 21, 467, (1968)
[8] Hirota, Ryogo; Satsuma, Junkichi, Prog. theor. phys. suppl., 59, 64, (1976)
[9] Krishnan, E.V., J. phys. soc. jpn., 51, 2391, (1982)
[10] Sawada, K.; Kotera, T., Progr. theor. phys., 51, 1355, (1974)
[11] Ramani, A., (), 54
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.