Whitham Gap Dynamics of the Real-Valued Solution of the Sine-Gordon Equation with Finite-Gap Boundary Conditions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 30 (1996) no. 4, pp. 31-44.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{FAA_1996_30_4_a3,
     author = {V. Yu. Novokshenov},
     title = {Whitham {Gap} {Dynamics} of the {Real-Valued} {Solution} of the {Sine-Gordon} {Equation} with {Finite-Gap} {Boundary} {Conditions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {31--44},
     publisher = {mathdoc},
     volume = {30},
     number = {4},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_1996_30_4_a3/}
}
TY  - JOUR
AU  - V. Yu. Novokshenov
TI  - Whitham Gap Dynamics of the Real-Valued Solution of the Sine-Gordon Equation with Finite-Gap Boundary Conditions
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 1996
SP  - 31
EP  - 44
VL  - 30
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_1996_30_4_a3/
LA  - ru
ID  - FAA_1996_30_4_a3
ER  - 
%0 Journal Article
%A V. Yu. Novokshenov
%T Whitham Gap Dynamics of the Real-Valued Solution of the Sine-Gordon Equation with Finite-Gap Boundary Conditions
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 1996
%P 31-44
%V 30
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_1996_30_4_a3/
%G ru
%F FAA_1996_30_4_a3
V. Yu. Novokshenov. Whitham Gap Dynamics of the Real-Valued Solution of the Sine-Gordon Equation with Finite-Gap Boundary Conditions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 30 (1996) no. 4, pp. 31-44. http://geodesic.mathdoc.fr/item/FAA_1996_30_4_a3/

[1] Zakharov V. E, Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov, Nauka, M., 1980 | MR

[2] Forest M. G., McLaughlin D. V., “Modulation of sinh-Gordon and sine-Gordon wavetrains”, Stud. Appl. Math., 68 (1983), 11–60 | DOI | MR

[3] Bikbaev R. F., Novokshenov V. Yu., “Self-similar solutions of the Whitham equations and Korteweg–de Vries equations with finite-gap boundary conditions”, Nonlinear and turbulent processes in physics, Proc. III Intern. Workshop. V. 1, Kiev, 1986, 32–35 | MR

[4] Bikbaev R. F., Novokshenov V. Yu., “Uravnenie KdF s konechnozonnymi granichnymi usloviyami i odnoparametricheskie resheniya uravnenii Uizema”, Asimptoticheskie svoistva reshenii differentsialnykh uravnenii, Ufa, 1989, 3–35 | MR

[5] Bikbaev R. F., Sharipov R. A., “Asimptotika resheniya zadachi Koshi dlya uravneniya Kortevega–de Friza v klasse potentsialov s konechnozonnym povedeniem pri $t\to\infty$”, Teoret. matem. fiz., 78 (1989), 345–356 | MR | Zbl

[6] Levermore D., “Hyperbolic structure of the KdV zero dispersion limit”, Commun. Partial Diff. Equat., 13 (1988), 485–511 | MR

[7] Bikbaev R. F., “Perestroika Uizema i vremennáya asimptotika resheniya nelineinogo uravneniya Shrëdingera s konechnozonnym povedeniem pri $x\to\pm\infty$”, Algebra i analiz, 2 (1990), 131–143 | MR

[8] Bikbaev R. F., Kuksin S. B., “Periodicheskaya granichnaya zadacha dlya uravneniya sinus-Gordon, ego malye gamiltonovy vozmuscheniya i KAM-teoriya dlya konechnozonnykh torov”, Algebra i analiz, 4 (1992), 42–78 | MR

[9] Date E., “Multi-soliton and quasi-periodic solution of nonlinear equations of sine-Gordon type”, Osaka J. Math., 19 (1982), 125–158 | MR | Zbl

[10] Erkolani N., Forest M. G., “On the manifold of real quasi-periodic sine-Gordon solutions”, Commun. Math. Phys., 99 (1985), 3–48 | MR

[11] Dubrovin B. A., Natanzon S. M., “Veschestvennye dvukhzonnye resheniya uravneniya sine-Gordon”, Funkts. analiz i ego pril., 16 (1982), 27–43 | MR | Zbl

[12] Springer Dzh., Rimanovy poverkhnosti, Mir, M., 1975

[13] Novokshenov V. Yu., “Uizemovskie deformatsii integriruemykh sistem tipa volchkov”, Funkts. analiz i ego pril., 27:2 (1993), 50–62 | MR | Zbl

[14] Dubrovin B. A., Novikov S. P., “Gidrodinamika slabo deformirovannykh solitonnykh reshetok. Differentsialnaya geometriya i gamiltonova teoriya”, UMN, 44 (1989), 29–98 | MR | Zbl

[15] Krichever I. M., “Metod usredneniya dlya dvumernykh integriruemykh uravnenii”, Funkts. analiz i ego pril., 22 (1988), 37–52 | MR | Zbl

[16] Kamchatnov A. M., “Nelineinye periodicheskie volny v vynuzhdennom kombinatsionnom rasseyanii sveta i rozhdenie solitonov na fronte impulsa”, ZhETF, 109 (1996), 786–804 | MR

[17] Bikbaev R. F., Kudashev V. R., “Example of shock waves in unstable media: the focusing nonlinear Schrödinger equation”, Phys. Lett. A, 190 (1994), 255–258 | DOI | MR | Zbl

[18] Gurevich A. V., Krylov A. L., El G. A., “Evolyutsiya rimanovoi volny v dispersionnoi gidrodinamike”, ZhETF, 101 (1992), 1797–1807 | MR

[19] El' G. A., Gurevich A. V., Khodorovskii V. V., Krylov A. L., “Modulation instability and formation of a nonlinear oscillatory structure in a “focusing” medium”, Phys. Lett. A, 177 (1992), 357–361

[20] Krichever I. M., “The periodic problem for two-dimensional integrable system”, Proc. Int. Congress of Math., Springer, Kyoto, 1991, 1353–1362 | MR

[21] Krichever I. M., “The dispersionless Lax equations and topological minimal models”, Commun. Math. Phys., 143 (1992), 415–429 | DOI | MR | Zbl

[22] Forest M. G., Sinha A., “A numerical study of nearly integrable modulation equations”, Singular Limits of Dispersive Waves, eds. N. Ercolani et al., Plenum, New York, 1994, 39–52. | DOI | MR | Zbl

[23] Bronski J. C., McLaughlin D. W., “Semiclassical behavior in the NLS equation, optical shocks–focusing instabilities”, Singular Limits of Dispersive Waveseds. . N. Ercolani et al., Plenum, New York, 1994, 12–25 | MR

[24] Potemin G. V., “Algebrogeometricheskie konstruktsii avtomodelnykh reshenii uravnenii Uizema”, UMN, 43:5 (1988), 252–253 | MR