In this work, the inverse spectral problem method is applied to integrate an equation composed of a combination of nonlinear KdV(+1) and KdV(-1) equations with an integral source. An infinite system of Dubrovin differential equations is derived to describe the evolution of the spectral data of the Hill operator. The solvability of the Cauchy problem for the infinite system of Dubrovin differential equations in the class of four times continuously differentiable periodic infinitely-gap functions is proved. An algorithm for finding infinite-gap periodic solutions of the mixed problem for the nonlinear KdF(+1) – KdF(-1) equation with an integral source is proposed, and a single-gap solution of this nonlinear system of equations is found explicitly, in terms of the Weierstrass elliptic function.
| Mualliflar | F. Ermamatova, G. Khasanov |
|---|---|
| Jurnal | Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi |
| Nashriyot | Самарқанд давлат университети |
| ISSN | 2091-5446, 2181-1296 |
| Nashr sanasi | 2026-07-01 |
| Jild | 2 |
| Son | 3 |
| Betlar | 65-73 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.59251/2181-3973.2025.v1.138.1.3957 |
| Indeksga qo‘shilgan | 2026-09-02 |
DOI: 10.59251/2181-3973.2025.v1.138.1.3957 · Maqolaning asl sahifasi
| APA | F. Ermamatova, & G. Khasanov (2026). INTEGRATION OF THE EQUATION COMPOSED OF A COMBINATION OF NONLINEAR KDV(+1) AND KDV(-1) EQUATIONS WITH AN INTEGRAL SOURCE. Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 2(3), 65-73. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3957 |
|---|---|
| GOST (OAK) | F. Ermamatova, G. Khasanov INTEGRATION OF THE EQUATION COMPOSED OF A COMBINATION OF NONLINEAR KDV(+1) AND KDV(-1) EQUATIONS WITH AN INTEGRAL SOURCE // Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi. – 2026. – T. 2, № 3. – P. 65-73. – DOI: 10.59251/2181-3973.2025.v1.138.1.3957. |
| MLA | F. Ermamatova, and G. Khasanov. “INTEGRATION OF THE EQUATION COMPOSED OF A COMBINATION OF NONLINEAR KDV(+1) AND KDV(-1) EQUATIONS WITH AN INTEGRAL SOURCE.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 2(3), 65-73, 2026. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3957 |
| Chicago | F. Ermamatova, and G. Khasanov. “INTEGRATION OF THE EQUATION COMPOSED OF A COMBINATION OF NONLINEAR KDV(+1) AND KDV(-1) EQUATIONS WITH AN INTEGRAL SOURCE.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 2(3), 65-73 (2026). https://doi.org/10.59251/2181-3973.2025.v1.138.1.3957 |
| Harvard | F. Ermamatova, and G. Khasanov (2026) ‘INTEGRATION OF THE EQUATION COMPOSED OF A COMBINATION OF NONLINEAR KDV(+1) AND KDV(-1) EQUATIONS WITH AN INTEGRAL SOURCE’, Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 2(3), 65-73. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3957 |
| BibTeX | @article{fermamatova2026,
title = {INTEGRATION OF THE EQUATION COMPOSED OF A COMBINATION OF NONLINEAR KDV(+1) AND KDV(-1) EQUATIONS WITH AN INTEGRAL SOURCE},
author = {F. Ermamatova and G. Khasanov},
journal = {Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi},
year = {2026},
volume = {2},
number = {3},
pages = {65-73},
doi = {10.59251/2181-3973.2025.v1.138.1.3957},
url = {https://doi.org/10.59251/2181-3973.2025.v1.138.1.3957}
} |
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