Geodesic
Integrable two-dimensional Lorentz-invariant nonlinear model of a complex scalar field (complex sine-Gordon II)
Teoretičeskaâ i matematičeskaâ fizika, Tome 48 (1981) no. 1, pp. 13-23 
B. S. Getmanov. Integrable two-dimensional Lorentz-invariant nonlinear model of a complex scalar field (complex sine-Gordon II). Teoretičeskaâ i matematičeskaâ fizika, Tome 48 (1981) no. 1, pp. 13-23. http://geodesic.mathdoc.fr/item/TMF_1981_48_1_a1/
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     title = {Integrable two-dimensional {Lorentz-invariant} nonlinear model of a~complex scalar field (complex {sine-Gordon~II)}},
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A study is made of the new two-dimensional nonlinear model of a complex scalar field (“complex sine-Gordon II”) which was discovered earlier by the author and can be integrated by the inverse scattering technique. The corresponding linear spectral problem is found and formulated in terms of the matrices of the algebra of the group $SU(3)$. The model has two types of soliton solutions which have vanishing and nonvanishing asymptotic behavior at infinity. An infinite series of integrable Lorentz-invariant systems that generalize the sine-Gordon equation is also obtained; when the first of them is reduced to Lagrangian form, it is identical with the model studied in the present paper.

[1] Getmanov B. S., Two-dimensional field theory models with higher integrals of motion, Preprint E2-80-319, JINR, Dubna, 1980

[2] Pohlmyer K., “Integrable Hamiltonian systems”, Commun. Math. Phys., 46 (1976), 207–221 | DOI | MR

[3] Getmanov B. S., “Novaya lorents-invariantnaya sistema s tochnymi mnogosolitonnymi resheniyami”, Pisma ZhETF, 25:2 (1977), 132–136; “Интегрируемая модель нелинейного комплексного скалярного поля”, ТМФ, 38:2 (1979), 186–194 | MR

[4] Lund F., Regge T., “Unified approach to strings and vortices”, Phys. Rev., 14:6 (1976), 1524–1535 | MR | Zbl

[5] Wadati M., “Invariances and conservation laws of the $\mathrm{K}-\mathrm{dV}$ equation”, Stud. Appl. Math., 59 (1978), 153–186 | DOI | MR | Zbl

[6] Ibragimov N. Kh., Shabat A. B., “Uravnenie K$-$deF s gruppovoi tochki zreniya”, DAN SSSR, 244:1 (1979), 57–61 | MR | Zbl

[7] Zhiber A. V., Shabat A. B., “Uravneniya Kleina-Gordona s netrivialnoi gruppoi”, DAN SSSR, 247:5 (1979), 1103–1107 | MR

[8] Getmanov B. S., Vzaimodeistvie solitonov uravneniya Kleina-Gordona, Preprint R2-10208, OIYaI, Dubna, 1976

[9] Kuznetsov E. A., Mikhailov A. V., “O polnoi integriruemosti dvumernoi klassicheskoi modeli Tirringa”, TMF, 30:3 (1977), 303–314 | MR

[10] Zakharov V. E., Shabat A. B., “Integrirovanie nelineinykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi”, Funktsionalnyi analiz, 13:3 (1979), 13–22 | MR | Zbl

[11] Zakharov V. E., Glava v kn.: Kunin I. A., Teoriya uprugikh sred s mikrostrukturoi, Mir, M., 1976 | MR

[12] Bogomolnyi E. B., “Stabilnost klassicheskikh reshenii”, YaF, 24 (1977), 861–872 | MR

[13] Hirota R., Lecture Notes in Mathematics, 515, 1976, 40–68 | DOI | MR | Zbl

[14] Zakharov V. E., Mikhailov A. V., “Dvumernye integriruemye modeli teorii polya”, ZhETF, 74:6 (1978), 1953–1973 | MR

[15] Budagov A. S., “Vpolne integriruemaya dvumernaya model teorii polya s netrivialnym vzaimodeistviem chastits”, Zap. nauchn. seminarov LOMI, 77 (1978), 24–56 | MR | Zbl