Geodesic
On Integration of One Class of Systems of Lax-Type Equations
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 1, pp. 45-62 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A nonlinear system of Lax-type equations is studied. The system is the basis of the construction of triangular models for commutative systems of linear non-selfadjoint bounded operators. Some of its solutions for $n=4$ are described. In one of the cases, the general solution is explicitly expressed in terms of special (elliptic) functions. 
@article{JMAG_2015_11_1_a2,
     author = {A. A. Lunyov and E. V. Oliynyk},
     title = {On {Integration} of {One} {Class} of {Systems} of {Lax-Type} {Equations}},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {45--62},
     year = {2015},
     volume = {11},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a2/}
}
TY  - JOUR
AU  - A. A. Lunyov
AU  - E. V. Oliynyk
TI  - On Integration of One Class of Systems of Lax-Type Equations
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2015
SP  - 45
EP  - 62
VL  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a2/
LA  - en
ID  - JMAG_2015_11_1_a2
ER  - 
%0 Journal Article
%A A. A. Lunyov
%A E. V. Oliynyk
%T On Integration of One Class of Systems of Lax-Type Equations
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2015
%P 45-62
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a2/
%G en
%F JMAG_2015_11_1_a2
A. A. Lunyov; E. V. Oliynyk. On Integration of One Class of Systems of Lax-Type Equations. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 1, pp. 45-62. http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a2/

[1] V. Ye. Zaharov, S. V. Manakov, S. P. Novikov, L. P. Pitayevsky, Soliton Theory, Nauka, M., 1980 (Russian) | MR

[2] V. A. Zolotarev, “Spectral Analisys of Non-selfadjoint Commutative Operator Systems and Nonlinear Differential Equations”, Resp. sb., Teor. Funktsij, Funkts. Analiz, i ih pril., 40, Kharkov, 1983, 68–71 (Russian) | MR | Zbl

[3] V. A. Zolotarev, “Time Cones and Functional Model on Riemann Surface”, Mat. Sb., 181:7 (1990), 965–994 (Russian) | MR

[4] V. A. Zolotarev, Analitical Methods of Spectral Representations of Non-selfadjoint and Non-unitary Operators, KhNU, Kharkov, 2003 (Russian)

[5] P. D. Lax, “Integrals of Nonlinear Equations of Evolution and Solitary Waves”, Commun. Pure Appl. Math., 21 (1968), 467–490 | DOI | MR | Zbl

[6] M. S. Livs̆ic, A. A. Yantsevich, Operator Colligations in Hilbert Spaces, Winston, Washington, D. C., 1979 (distributed by Wiley, New York) | MR | Zbl

[7] A. A. Lunyov, E. V. Oliynyk, “On One Class of System of Lax-type Equations”, UMV, 10:4 (2013), 507–531 (Russian) | MR