ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Zhuravlev V. M. Exactly integrable models of the wave interaction with continuous spectrum. Izvestiya VUZ. Applied Nonlinear Dynamics, 2001, vol. 9, iss. 2, pp. 76-81. DOI: 10.18500/0869-6632-2001-9-2-76-81

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Language: 
Russian
Article type: 
Article
UDC: 
5301

Exactly integrable models of the wave interaction with continuous spectrum

Autors: 
Zhuravlev Viktor Mikhailovich, Ulyanovsk State University
Abstract: 

Interaction with a continuous spectrum in inhomogeneous media is constructed the Laks representation of exactly integrable model of the wave by the generalized Lagrange identities method for the conjugated equations. The general analysis of the obtained equations and ways of their use in theoretical and applied physical problems of non-linear wave processes are carried out.

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Acknowledgments: 
The work was supported by the Russian Foundation for Basic Research (project № 00-01-00260)
Reference: 
  1. Zakharov BE, Manakov CB. To the theory of resonance interaction of wave packets in nonlinear media. J. Exp. Theor. Phys. 1975:69(5):1654–1673.
  2. Zakharov BE, Manakov CB, Novikov SP, Pitaevsky LP. Theory of Solitons: Method of Inverse Problem; Moscow: Nauka; 1980. 320 pp.
  3. Zhuravlev VM. Accurately integrable model of three-wave interaction in inhomogeneous nonlinear medium. JETP Lett. 1995:61(4):254–258.
  4. Zhuravlev VM. Models of nonlinear wave processes admitting soliton solutions. J. Exp. Theor. Phys. 1996;110(6):2243.  
  5. Sukhorukov AP. Nonlinear wave processes of interaction in optics and radiophysics. Moscow: Nauka; 1998. 232 p.
  6. Izyurov CA, Kozlov CA. Dynamics of the spatial spectrum of a light wave at its self-focusing in a nonlinear medium. JETP Lett. 2000;71(11):666–670.
  7. Zakharov VE. Method of the inverse scattering problem. Solitons. Moscow: Mir; 1983. 270 p.
  8. Zakharov VE, Manakov SV. Construction of higher-dimensional nonlinear integrable systems and of their solutions. Funct Anal Its Appl. 1985;19(2):89–101. DOI: 10.1007/BF01078388
Received: 
20.12.2000
Accepted: 
11.03.2001
Published: 
17.07.2001