equations with self-consistent source, inverse scattering method.
UDC:
517.9, 517.946
Subject:
Integration of nonlinear evolution equation with self-consistent source.
Main publications:
A. B. Khasanov, G. U. Urazboev, On the General Korteweg–de Vries Equation with a Source in the Class of Steplike Functions, Dokl. Math., 2004, 70:1, 512–516.
A. B. Khasanov, G. U. Urasboev, On the sine-Gordon equation with a self-consistent source corresponding to multiple eigenvalues, Differential Equations, 2007, 43:4, 561–570.
G. U. Urazboev, I. I. Baltaeva, O. B. Ismoilov, “Scattering theory for the loaded negative order Korteweg–de Vries equation”, Chebyshevskii Sb., 25:2 (2024), 169–180
2.
Gayrat U. Urazboev, Iroda I. Baltaeva, Shoira E. Atanazarova, “Soliton solutions of the negative order modified Korteweg – de Vries equation”, Bulletin of Irkutsk State University. Series Mathematics, 47 (2024), 63–77
3.
G. U. Urazboev, M. M. Khasanov, O. B. Ismoilov, “Integration of negative-order modified Korteweg–de Vries equation with an integral source”, Izv. IMI UdGU, 63 (2024), 80–90
4.
G. U. Urazboev, I. I. Baltaeva, A. K. Babadjanova, “Soliton solutions of the negative-order nonlinear Schrödinger equation”, TMF, 219:2 (2024), 263–273; Theoret. and Math. Phys., 219:2 (2024), 761–769
2023
5.
Gayrat U. Urazboev, Muzaffar M. Khasanov, Iroda I. Baltaeva, “Integration of the negative order Korteweg-de Vries equation with a special source”, Bulletin of Irkutsk State University. Series Mathematics, 44 (2023), 31–43
G. U. Urazboev, A. B. Yakhshimuratov, M. M. Khasanov, “Integration of negative-order modified Korteweg–de Vries equation in a class of periodic functions”, TMF, 217:2 (2023), 317–328; Theoret. and Math. Phys., 217:2 (2023), 1689–1699
G. U. Urazboev, I. I. Baltaeva, O. B. Ismoilov, “Integration of the negative order Korteweg–de Vries equation by the inverse scattering method”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:3 (2023), 523–533
Michal Fečkan, Gayrat Urazboev, Iroda Baltaeva, “Inverse scattering and loaded modified Korteweg-de Vries equation”, J. Sib. Fed. Univ. Math. Phys., 15:2 (2022), 176–185
9.
G. U. Urazboev, I. I. Baltaeva, “Integration of Camassa-Holm equation with a self-consistent source of integral type”, Ufimsk. Mat. Zh., 14:1 (2022), 84–94; Ufa Math. J., 14:1 (2022), 77–86
G. U. Urazboev, M. M. Hasanov, “Integration of the negative order Korteweg-de Vries equation with a self-consistent source in the class of periodic functions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:2 (2022), 228–239
G. U. Urazboev, A. A. Reyimberganov, A. K. Babadjanova, “Integration of the matrix nonlinear Schrödinger equation with a source”, Bulletin of Irkutsk State University. Series Mathematics, 37 (2021), 63–76
G. U. Urazboev, I. I. Baltaeva, I. D. Rakhimov, “A generalized $(G'/G)$-expansion method for the loaded
Korteweg—de Vries equation”, Sib. Zh. Ind. Mat., 24:4 (2021), 139–147
G. U. Urazboev, A. K. Babadjanova, D. R. Saparbaeva, “Integration of the Harry Dym equation with an integral type source”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:2 (2021), 285–295
G. U. Urazboev, U. A. Xoitmetov, A. K. Babadjanova, “Integration of the matrix modified Korteweg–de Vries equation with an integral-type source”, TMF, 203:3 (2020), 351–364; Theoret. and Math. Phys., 203:3 (2020), 734–746
I. I. Baltaeva, G. U. Urazboev, “About the Camassa–Holm equation with a self-consistent source”, Ufimsk. Mat. Zh., 3:2 (2011), 10–19; Ufa Math. J., 3:2 (2011), 10–18
A. B. Khasanov, G. U. Urazboev, “Integration of the sine-Gordon equation with a self-consistent source of the integral type in the case of multiple eigenvalues”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 3, 55–66; Russian Math. (Iz. VUZ), 53:3 (2009), 45–55
A. B. Khasanov, G. U. Urazboev, “On the sine-Gordon equation with a self-consistent source”, Mat. Tr., 11:1 (2008), 153–166; Siberian Adv. Math., 19:1 (2009), 13–23
A. B. Khasanov, G. U. Urazboev, “On the Sine–Gordon equation with a self-consistent source of the integral type”, Zh. Mat. Fiz. Anal. Geom., 2:3 (2006), 287–298
A. B. Khasanov, G. U. Urazboev, “The solution of general KdV equation in a class of steplike functions”, Zap. Nauchn. Sem. POMI, 317 (2004), 174–199; J. Math. Sci. (N. Y.), 136:1 (2006), 3625–3640
G. U. Urazboev, A. B. Khasanov, “Integrating the Korteweg–de Vries Equation with a Self-Consistent Source and “Steplike” Initial Data”, TMF, 129:1 (2001), 38–54; Theoret. and Math. Phys., 129:1 (2001), 1341–1356