Tenglamalar sistemasini qaraymiz. Bu yerda

Teorema 2.2.1. Agar funksiyalar (1)-(6) masalaning yechimlari bo’lsa, u holda potentsiali bo’lgan operatorning sochilish nazariyasining berilganlari bo’yicha quyidagicha o’zgaradi:

Oхirgi tengliklar yordamida larni anihlash mumkin.

ADABIYOTLAR
1. Gardner C.S., Green I.M., Kruskal M.D., Miura R.M. Method for solving the      Korteweg-de Vries equation, Phys. Rev. Lett., 19 (1967), 1095-1097.

2. Laks P.D. Integralы nelineynых evolyutsionnых uravneniy i uedinennыe  volnы, Matematika (1969), t. 13, 128-150.

3. Zaхarov V.E., SHabat A.B., Tochnaya teoriya dvumernoy samofokusirovki i odnomernoy avtomodulyatsii voln v nelineynых sredaх, JETF, 1971, t. 61, s. 118.

4. Ablovits M., Sigur Х. Solitonы i metod obratnoy zadachi, M: Mir, 1987.

5.Ablowitz M.J., Kaup D.J., Newell A.C., Segur H., - Stud. Appl.Math. 53, 249     (1974).

6. Taхtadjyan L.A., Faddeev L.D. Gamilьtonov podхod v teorii soliton      solitonov. M:Nauka.

7. Melьnikov V.K. Metod integrirovaniya uravneniya Kortevega-de Vrisa s      samosoglasovannыm istochnikom. Preprint OIYAI R2-88-373, Dubna, 1988.

8. Melnikov V.K. Creation and annihilation of solitons in the system    described   by the KdV equation with a self-consistent source.    Inv.Probl., 6, (1990),   809-823.

9. Melnikov V.K. Integration of the KdV equation with a source.    Inv.Probl., 5,      (1991), 233-246.

10. Leon J., Latifi A. Solution of an initial-boundry value problem for coupled      nonlinear waves. J.Phys.A: Math.Gen. 23 (1990), 1385 – 1403.

11.Хasanov A.B., Urazbaev G.U. Integrirovanie uravneniya Kortevega-de     Friza s samosoglasovannыm istochnikom pri nachalьnых dannых tipa      stupenьki metodom obratnoy zadachi rasseyaniya.\\ Uzbekskiy      matematicheskiy jurnal. 2000 g., № 2, s. 56-66.

12.Urazbaev G.U. Ob integrirovanie uravneniya KdF s samosoglasovannыm     istochnikom pri nachalьnых dannых tipa stupenьki. \\ Dokladы AN RUz.     2000 g., № 5, s. 3-7.

13.Хasanov A.B., Urazbaev G.U. Ob integrirovanie uravneniya KdF s      samosoglasovannыm istochnikom pri nachalьnых dannых tipa stupenьki.

 \\Trudы mejdunarodnoy konferentsii «Simmetriya i differentsialьnыe     uravneniya». g. Krasnoyarsk (Rossiya), 2000 g., s. 248-251.

14. Da-jun Zhang. The N-soliton Solutions for the Modified KdV eqution with self-consistent sources. Journal of the Physical Society of Japan Vol. 71, № 11, November, 2002, pp.2649-2656.

15. Da-jun Zhang, Deng-yuan Chen. The N-soliton Solutions for the Sine-Gordon eqution with self-consistent sources. Physica A 32/ (2003) 467-481.

16. M.G.Gasыmov. Obratnaya zadacha teorii rasseyaniya dlya sistemы uravneniy Diraka poryadka 2n TMMO t. 19, 1968.

17. L.P.Nijnik. Fam Loy Vu. Obratnaya zadacha rasseyaniya na polulsu s nesamosopryajennoy potentsialbnoy matritsey. UMJ t. 26, №4. (1974), 469-486.

18. Evgrafor M.A. Analiticheskie funktsii. M. Nauka, 1968 g.

19. Sveshnikov A.G., Tiхonov A.N. Teoriya funktsiy kompleksnoy peremennoy. M. Nauka, 1970. Str.128-130.

20. Wadati M., J. Phys. Soc. Japan 32 (1972), 1681.

21.Mamedov K.A., Reyimberganov A.A. Ob integrirovanii modifitsirovannogo uravneniya Kortevega-de Friza s istochnikom. Trudы mej.konf. 18-24 aprelya. Toshkent-2005. Str.108-110.