|
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References
|
|
| |
| 1. |
Wadati M., “The exact solution of the modified Korteweg-de Vries equation”, Journal of the Physical Society of Japan, 32:6 (1972), 1681–1681   |
| 2. |
Leblond H., Sanchez F., “Models for optical solitons in the two-cycle regime”, Physical Review A, 67:1 (2003), 013804 |
| 3. |
Leblond H., Mihalache D., “Models of few optical cycle solitons beyond the slowly varying envelope approximation”, Physics Reports, 523:2 (2013), 61–126 |
| 4. |
Ono H., “Soliton fission in anharmonic lattices with reflectionless inhomogeneity”, Journal of the Physical Society of Japan, 61:12 (1992), 4336–4343 |
| 5. |
Kakutani T., Ono H., “Weak non-linear hydromagnetic waves in a cold collision-free plasma”, Journal of the Physical Society of Japan, 26:5 (1969), 1305–1318 |
| 6. |
Konno K., Ichikawa Y.H., “A modified Korteweg-de Vries equation for ion acoustic waves”, Journal of the Physical Society of Japan, 37:6 (1974), 1631–1636 |
| 7. |
Watanabe S., “Ion acoustic soliton in plasma with negative ion”, Journal of the Physical Society of Japan, 53:3 (1984), 950–956 |
| 8. |
Lonngren K.E., “Ion acoustic soliton experiment in a plasma”, Optical and Quantum Electronics, 30 (1998), 615–630 |
| 9. |
Ziegler V., Dinkel J., Setzer C., Lonngren K.E., “On the propagation of nonlinear solitary waves in a distributed Schottky barrier diode transmission line”, Chaos, Solitons and Fractals, 12:9 (2001), 1719–1728  |
| 10. |
Cushman-Roisin B., Pratt L., Ralph E., “A general theory for equivalent barotropic thin jets”, Journal of Physical Oceanography, 23:1 (1993), 91–103 |
| 11. |
Ralph E.A., Pratt L., “Predicting eddy detachment for an equivalent barotropic thin jet”, Journal of Nonlinear Science, 4:1 (1994), 355–374 |
| 12. |
Grimshaw R., Pelinovsky E., Talipova T., Kurkin A., “Simulation of the transformation of internal solitary waves on oceanic shelves”, Journal of Physical Oceanography, 34:12 (2004), 2774–2779 |
| 13. |
Grimshaw R., “Internal solitary waves”, Environmental stratified flows, Springer, New York, 2002, 1–27 |
| 14. |
Tappert F.D., Varma C.M., “Asymptotic theory of self-trapping of heat pulses in solids”, Physical Review Letters, 25:16 (1970), 1108–1111 |
| 15. |
Hirota R., “Exact solution of the modified Korteweg-de Vries equation for multiple collisions of solitons”, Journal of the Physical Society of Japan, 33:5 (1972), 1456–1458 |
| 16. |
Satsuma J., “A Wronskian representation of $N$-soliton solutions of nonlinear evolution equations”, Journal of the Physical Society of Japan, 46:1 (1979), 359–360 |
| 17. |
Nimmo J.J.C., Freeman N.C., “The use of Backlund transformations in obtaining $N$-soliton solutions in Wronskian form”, Journal of Physics A: Mathematical and General, 17:7 (1984), 1415–1424 |
| 18. |
Gesztesy T., Schweiger W., “Rational $KP$ and $mKP$-solutions in Wronskian form”, Reports on Mathematical Physics, 30:2 (1991), 205–222 |
| 19. |
Khasanov A.B., Urazbayev G.U., “Method for solving the mKdV equation with a self-consistent source”, Uzbek Mathematical Journal, 2003, no. 1, 69–75 (in Russian) |
| 20. |
Urazbayev G.U., “On the modified KdV equation with a self-consistent source corresponding to multiple eigenvalues”, Reports of the Academy of Sciences of the Republic of Uzbekistan, 2005, no. 5, 11–14 (in Russian) |
| 21. |
Mamedov K.A., “On the integration of the modified Korteweg-de Vries equation with a source of integral type”, Reports of the Academy of Sciences of the Republic of Uzbekistan, 2006, no. 2, 24–28 (in Russian) |
| 22. |
Demontis F., “Exact solutions of the modified Korteweg-de Vries equation”, Theoretical and Mathematical Physics, 168:1 (2011), 886–897  |
| 23. |
Mamedov K.A., “Integration of mKdV equation with a self-consistent source in the class of finite density functions in the case of moving eigenvalues”, Russian Mathematics, 64:10 (2020), 66–78 |
| 24. |
Wu Jianping, Geng Xianguo, “Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation”, Communications in Nonlinear Science and Numerical Simulation, 53 (2017), 83–93 |
| 25. |
Zhang Guoqiang, Yan Zhenya, “Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions”, Physica D: Nonlinear Phenomena, 410 (2020), 132521 |
| 26. |
Vaneeva O., “Lie symmetries and exact solutions of variable coefficient mKdV equations: An equivalence based approach”, Communications in Nonlinear Science and Numerical Simulation, 17:2 (2012), 611–618 |
| 27. |
Ablowitz M.J., Sigur H., Solitons and the inverse scattering transform, SIAM, Philadelphia, 1981 |
| 28. |
Dodd R.K., Eilbeck J.C., Gibbon J.D., Morris H.C., Solitons and nonlinear wave equations, Academic Press, London, 1982 |
| 29. |
Nakhushev A.M., Equations of mathematical biology, Vysshaya Shkola, Moscow, 1995 |
| 30. |
Nakhushev A.M., “Loaded equations and their applications”, Differentsial'nye Uravneniya, 19:1 (1983), 86–94 (in Russian) |
| 31. |
Kozhanov A.I., “Nonlinear loaded equations and inverse problems”, Computational Mathematics and Mathematical Physics, 44:4 (2004), 657–678 |
| 32. |
Hasanov A.B., Hoitmetov U.A., “On integration of the loaded Korteweg-de Vries equation in the class of rapidly decreasing functions”, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 47:2 (2021), 250–261 |
| 33. |
Hoitmetov U.A., “Integration of the loaded KdV equation with a self-consistent source of integral type in the class of rapidly decreasing complex-valued functions”, Siberian Advances in Mathematics, 33:2 (2022), 102–114 |
| 34. |
Khasanov A.B., Hoitmetov U.A., “Integration of the general loaded Korteweg-de Vries equation with an integral type source in the class of rapidly decreasing complex-valued functions”, Russian Mathematics, 65:7 (2021), 43–57 |
| 35. |
Khasanov A.B., Hoitmetov U.A., “On complex-valued solutions of the general loaded Korteweg-de Vries equation with a source”, Differensial Equations, 58:3 (2022), 381–391 |
| 36. |
Hoitmetov U., “Integration of the loaded general Korteweg-de Vries equation in the class of rapidly decreasing complex-valued functions”, Eurasian Mathematical Journal, 13:2 (2022), 43–54 |
| 37. |
Khasanov A.B., Hoitmetov U.A., “On integration of the loaded mKdV equation in the class of rapidly decreasing functions”, Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya «Matematika», 38 (2021), 19–35 |
| 38. |
Hoitmetov U.A., “Integration of the sine-Gordon equation with a source and an additional term”, Reports on Mathematical Physics, 90:2 (2022), 221–240 |
