|
|
|
|
СПИСОК ЛИТЕРАТУРЫ
|
|
| |
| 1. |
Boussinesq J., “Théorie de l'intumescence liquide appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire”, Comptes rendus hebdomadaires des séances de l'Académie des Sciences, 72 (1871), 755–759 |
| 2. |
Kaup D. J., “A higher-order water-wave equation and the method for solving it”, Progress of Theoretical Physics, 54:2 (1975), 396–408     |
| 3. |
Matveev V. B., Yavor M. I., “Solutions presque périodiques et a N-solitons de l'equation hydrodynamique non linéaire de Kaup”, Annales de l'I. H. P. Physique théorique, 31:1 (1979), 25–41 http://eudml.org/doc/76040 |
| 4. |
Смирнов А. О., “Вещественные конечнозонные регулярные решения уравнения Каупа–Буссинеска”, Теоретическая и математическая физика, 66:1 (1986), 30–46  ; Smirnov A. O., “Real finite-gap regular solutions of the Kaup–Boussinesq equation”, Theoretical and Mathematical Physics, 66:1 (1986), 19–31 |
| 5. |
Митропольский Ю. А., Боголюбов Н. Н. (мл.), Прикарпатский А. К., Самойленко В. Г., Интегрируемая динамическая система: спектральные и дифференциально-геометрические аспекты, Наукова думка, Киев, 1987 [Mitropol'skii Yu. A., Bogolyubov N. N. (Jr.), Prikarpatskii A. K., Samoilenko V. G., Integrable dynamical system: spectral and differential-geometric aspects, Naukova dumka, Kiev, 1987] |
| 6. |
Jaulent M., Miodek I., “Nonlinear evolution equation associated with ‘energy-dependent Schrödinger potentials’”, Letters in Mathematical Physics, 1:3 (1976), 243–250 |
| 7. |
Sattinger D. H., Szmigielski J., “Energy dependent scattering theory”, Differential and Integral Equations, 8:5 (1995), 945–959 |
| 8. |
Ivanov R., Lyons T., “Integrable models for shallow water with energy dependent spectral problems”, Journal of Nonlinear Mathematical Physics, 19 (2012), 72–88 |
| 9. |
Haberlin J., Lyons T., “Solitons of shallow-water models from energy-dependent spectral problems”, The European Physical Journal Plus, 133 (2018), 16 |
| 10. |
Wazwaz A.-M., “The generalized Kaup–Boussinesq equation: multiple soliton solutions”, Waves in Random and Complex Media, 25:4 (2015), 473–481 |
| 11. |
Chen Ch., Jiang Y.-L., “Invariant solutions and conservation laws of the generalized Kaup–Boussinesq equation”, Waves in Random and Complex Media, 29:1 (2019), 138–152 |
| 12. |
Li W.-H., Wang Y., “Exact dynamical behavior for a dual Kaup–Boussinesq system by symmetry reduction and coupled trial equations method”, Advances in Difference Equations, 2019 (2019), 451 |
| 13. |
Hosseini K., Ansari R., Gholamin P., “Exact solutions of some nonlinear systems of partial differential equations by using the first integral method”, Journal of Mathematical Analysis and Applications, 387:2 (2012), 807–814 |
| 14. |
Zhou J., Tian L., Fan X., “Solitary-wave solutions to a dual equation of the Kaup–Boussinesq system”, Nonlinear Analysis: Real World Applications, 11:4 (2010), 3229–3235 |
| 15. |
Mel'nikov V. K., “Integration method of the Korteweg–de Vries equation with a self-consistent source”, Physics Letters A, 133:9 (1988), 493–496 |
| 16. |
Mel'nikov V. K., “Integration of the Korteweg–de Vries equation with a source”, Inverse Problems, 6:2 (1990), 233–246 |
| 17. |
Leon J., Latifi A., “Solution of an initial-boundary value problem for coupled nonlinear waves”, Journal of Physics A: Mathematical and General, 23:8 (1990), 1385–1403 |
| 18. |
Claude C., Latifi A., Leon J., “Nonlinear resonant scattering and plasma instability: an integrable model”, Journal of Mathematical Physics, 32:12 (1991), 3321–3330 |
| 19. |
Mel'nikov V. K., “Integration of the nonlinear Schrödinger equation with a self-consistent source”, Communications in Mathematical Physics, 137:2 (1991), 359–381 |
| 20. |
Gerdjikov V. S., Grahovski G., Ivanov R., “On the integrability of KdV hierarchy with self-consistent sources”, Communications on Pure and Applied Analysis, 11:4 (2012), 1439–1452 |
| 21. |
Li Q., Zhang J. B., Chen D. Y., “The eigenfunctions and exact solutions of discrete mKdV hierarchy with self-consistent sources via the inverse scattering transform”, Advances in Applied Mathematics and Mechanics, 7:5 (2015), 663–674 |
| 22. |
Bondarenko N., Freiling G., Urazboev G., “Integration of the matrix KdV equation with self-consistent sources”, Chaos, Solitons and Fractals, 49 (2013), 21–27 |
| 23. |
Babadjanova A., Kriecherbauer T., Urazboev G., “The periodic solutions of the discrete modified KdV equation with a self-consistent source”, Applied Mathematics and Computation, 376 (2020), 125136 |
| 24. |
Urazboev G. U., Babadjanova A. K., Saparbaeva D. R., “Integration of the Harry Dym equation with an integral type source”, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 31:2 (2021), 285–295 |
| 25. |
Grinevich P. G., Taimanov I. A., “Spectral conservation laws for periodic nonlinear equations of the Melnikov type”, Geometry, Topology, and Mathematical Physics: S. P. Novikov's Seminar: 2006–2007, AMS, 2008, 125–138 |
| 26. |
Urazboev G., Babadjanova A., “On the integration of the matrix modified Korteweg–de Vries equation with self-consistent source”, Tamkang Journal of Mathematics, 50:3 (2019), 281–291 |
| 27. |
Yakhshimuratov A., “The nonlinear Schrödinger equation with a self-consistent source in the class of periodic functions”, Mathematical Physics, Analysis and Geometry, 14:2 (2011), 153–169 |
| 28. |
Babajanov B., Fečkan M., Urazbaev G., “On the periodic Toda lattice hierarchy with an integral source”, Communications in Nonlinear Science and Numerical Simulation, 52 (2017), 110–123 |
| 29. |
Бабажанов Б. А., Хасанов А. Б., “О периодической цепочке Тоды с интегральным источником”, Теоретическая и математическая физика, 184:2 (2015), 253–268 ; Babajanov B. A., Khasanov A. B., “Periodic Toda chain with an integral source”, Theoretical and Mathematical Physics, 184:2 (2015), 1114–1128 |
| 30. |
Huang Y., Zeng Y., Ragnisco O., “The Degasperis–Procesi equation with self-consistent sources”, Journal of Physics A: Mathematical and Theoretical, 41:35 (2008), 355203 |
| 31. |
Zeng Y.-B., Ma W.-X., Shao Y.-J., “Two binary Darboux transformations for the KdV hierarchy with self-consistent sources”, Journal of Mathematical Physics, 42:5 (2001), 2113–2128 |
| 32. |
Zeng Y.-B., Shao Y.-J., Ma W.-X., “Integral-type Darboux transformations for the mKdV hierarchy with self-consistent sources”, Communications in Theoretical Physics, 38:6 (2002), 641–648 |
| 33. |
Zeng Y.-B., Shao Y.-J., Xue W.-M., “Positon solutions of the KdV equation with self-consistent sources”, Theoretical and Mathematical Physics, 137:2 (2003), 1622–1631 |
| 34. |
Xiao T., Zeng Y.-B., “Generalized Darboux transformations for the KP equation with self-consistent sources”, Journal of Physics A: Mathematical and General, 37:28 (2004), 7143–7162 |
| 35. |
Gegenhasi, Xiaorong Bai, “On the modified discrete KP equation with self-consistent sources”, Journal of Nonlinear Mathematical Physics, 24:2 (2017), 224–238 |
| 36. |
Zhang D., “The $N$-soliton solutions of some soliton equations with self-consistent sources”, Chaos, Solitons and Fractals, 18:1 (2003), 31–43 |
| 37. |
Matsuno Y., “Bilinear Backlund transformation for the KdV equation with a source”, Journal of Physics A: Mathematical and General, 24:6 (1991), 273–277 |
| 38. |
Deng S.-F., Chen D.-Y., Zhang D.-J., “The multisoliton solutions of the KP equation with self-consistent sources”, Journal of the Physical Society of Japan, 72:9 (2003), 2184–2192 |
| 39. |
Zhang D.-J., Chen D.-Y., “The $N$-soliton solutions of the sine-Gordon equation with self-consistent sources”, Physica A: Statistical Mechanics and its Applications, 321:3–4 (2003), 467–481 |
| 40. |
Cabada A., Yakhshimuratov A., “The system of Kaup equations with a self-consistent source in the class of periodic functions”, Journal of Mathematical Physics, Analysis, Geometry, 9:3 (2013), 287–303 |
| 41. |
Yakhshimuratov A., Kriecherbauer T., Babajanov B., “On the construction and integration of a hierarchy for the Kaup system with a self-consistent source in the class of periodic functions”, Journal of Mathematical Physics, Analysis, Geometry, 17:2 (2021), 233–257 |
| 42. |
Jaulent M., “On an inverse scattering problem with an energy-dependent potential”, Annales de l'I. H. P. Physique théorique, 17:4 (1972), 363–378 http://eudml.org/doc/75763 |
| 43. |
Jaulent M., Jean C., “The inverse problem for the one-dimensional Schrödinger operator with an energy-dependent potential. I”, Annales de l'I. H. P. Physique théorique, 25:2 (1976), 105–118 http://eudml.org/doc/75912 |
| 44. |
Jaulent M., Jean C., “The inverse problem for the one-dimensional Schrödinger operator with an energy-dependent potential. II”, Annales de l'I. H. P. Physique théorique, 25:2 (1976), 119–137 http://eudml.org/doc/75913 |
| 45. |
Максудов Ф. Г., Гусейнов Г. Ш., “О решении обратной задачи рассеяния для квадратичного пучка одномерных операторов Шрёдингера на всей оси”, Докл. АН СССР, 289:1 (1986), 42–46 ; Maksudov F. G., Gusejnov G. Sh., “On solution of the inverse scattering problem for a quadratic pencil of one-dimensional Schrödinger operators on the whole axis”, Sov. Math., Dokl., 34 (1986), 34–38 |
| 46. |
Laptev A., Shterenberg R., Sukhanov V., “Inverse spectral problems for Schrödinger operators with energy depending potentials”, Probability and Mathematical Physics, A Volume in Honor of Stanislav Molchanov, AMS, 2007, 341–351 |
| 47. |
Aktosun T., Klaus M., van der Mee C., “Wave scattering in one dimension with absorption”, Journal of Mathematical Physics, 39:4 (1998), 1957–1992 |
| 48. |
Бабажанов Б. А., Хасанов А. Б., “Обратная задача для квадратичного пучка операторов Штурма–Лиувилля с конечнозонным периодическим потенциалом на полуоси”, Дифференциальные уравнения, 43:6 (2007), 723–730  ; Babazhanov B. A., Khasanov A. B., “Inverse problem for a quadratic pencil of Sturm–Liouville operators with finite-gap periodic potential on the half-line”, Differential Equations, 43:6 (2007), 737–744 |
| 49. |
Бабажанов Б. А., Хасанов А. Б., Яхшимуратов А. Б., “Об обратной задаче для квадратичного пучка операторов Штурма–Лиувилля с периодическим потенциалом”, Дифференциальные уравнения, 41:3 (2005), 298–305 ; Babadzhanov B. A., Khasanov A. B., Yakhshimuratov A. B., “On the inverse problem for a quadratic pencil of Sturm–Liouville operators with periodic potential”, Differential Equations, 41:3 (2005), 310–318 |
