SPEKTRAL ANALIZNING TESKARI MASALALARI VA ULARNING NOCHIZIQLI EVALYUSION TENGLAMALARGA TATBIQLARI SOHASI BO‘YICHA ETAKCHI MUTAXASSIS

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BOG'LANISH

YUTUQLAR, MUKOFOTLAR

Ilmiy maqollarining 43 tasi SCOPUS va Web of Sciencs bazalariga kiritilgan, h-index - 9.

XASANOV AKNAZAR BEKDURDIYEVICH

Fizika-matematika fanlari doktori, professor Differensial tenglamalar kafedrasi mudiri

Ilmiy tadqiqot yo‘nalishi:

Teskari spektral masalalar usulini nochiziqli kompleks modifitsirlangan Korteveg-de Friz, Shredinger, sinus-Gordon, Xirota tenglamalari cheksiz zonali davriy funksiyalar sinfida integrallashda qo‘llash.

Ilmiy tadqiqotlarining asosiy natijalari:

Teskari spektral masalalar usulidan foydalangan holda, uch marta uzluksiz differensiallanuvchi davriy cheksiz zonali funksiyalar sinfida giperbolik kosinus-Gordon tenglamasining integrallanuvchi ekanligi isbotlagan. Teskari spektral masalalar usulidan foydalangan holda, uch marta uzluksiz differensiallanuvchi davriy cheksiz zonali funksiyalar sinfida Xirota tipidagi nochiziqli xususiy hosilali differensial tenglamasining integrallanuvchi ekanligi isbotlagan. Teskari spektral masalalar usulidan foydalangan holda, uch marta uzluksiz differensiallanuvchi davriy cheksiz zonali funksiyalar sinfida modifitsirlangan Korteveg-de Friz-Sinus Gordon nochiziqli tenglamasining integrallanuvchi ekanligi isbotlagan. Teskari spektral masalalar usulidan foydalangan holda, uch marta uzluksiz differensiallanuvchi davriy cheksiz zonali funksiyalar sinfida yuklangan hadli nochiziqli defokuslangan Shredinger tenglamasining integrallanuvchi ekanligi isbotlagan. Shturm-Liuvill va Dirak operatorlari uchun izospektral chegaraviy masalalar oilasini tiklagan va ularni o’zgaruvchan koeffisiyentli giperbilik va parabolik tipli tenglamalarga qo’yilgan aralash masalalarni yechimini topishga tatbiq qilgan. Birinchi tartibli elliptik tipdagi tenglamalar sistemasi uchun Koshi masalasi yechimining regulyarizatsiyasini qurgan.

Asosiy ilmiy nashrlari:

Integration of a Nonlinear Hirota Type Equation with Finite Density in the Class of Periodic Functions. Khasanov, A., Eshbekov, R., Normurodov, K. Lobachevskii Journal of Mathematics, 2023, 44(10), 4329–4347
Khasanov, A.B., Normurodov K.N., Khudaerov, U.O. Integrating the modified Korteweg–de Vries– sine-Gordon equation in the class of periodic infinite-gap functions. Theoretical and Mathematical Physics(Russian Federation), 2023, 214(2), pp. 170–182.
Muminov, U.B., Khasanov, A.B. The Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with a Loaded Term. Siberian Advances in Mathematics, 2022, 32(4), pp. 277–298.
Khasanov, A.B., Khasanov T.G. Integration of a Nonlinear Korteweg–de Vries Equation with a Loaded Term and a Source. Journal of Applied and Industrial Mathematics, 2022, 16(2), pp. 227–239.
Khasanov, A.B., Allanazarova T.Z. On the Modified Korteweg–De-Vries Equation with Loaded Term. Ukrainian Mathematical Journal, 2022, 73(11), pp. 1783–1809.
Muminov, U.B., Khasanov A.B. Integration of a defocusing nonlinear Schrödinger equation with additional terms. Theoretical and Mathematical Physics(Russian Federation), 2022, 211(1), pp. 514–531.
Khasanov, A.B., Hoitmetov U.A. On Complex-Valued Solutions of the General Loaded Korteweg–de Vries Equation with a Source. Differential Equations, 2022, 58(3), pp. 381–391.
Hasanov, A.B., Babajanov B.A., Atajonov D.O. On the Integration of the Periodic Camassa-Holm Equation with a Self-Consistent Source. Journal of Siberian Federal University - Mathematics and Physics, 2022, 15(6), pp. 785–796.
Khasanov, A.B., Hoitmetov, U.A. Integration of the loaded Korteweg-de Vries equation with a self-consistent source in the class of rapidly decreasing complex-valued functions. Transactions Issue Mathematics, Azerbaijan National Academy of Sciences, 2022, 42(4), pp. 87–101.
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, 2021, 65(7), pp. 43–57.
Г.А.Маннонов, А.Б.Хасанов. Задача Коши для нелинейного уравнения Хирота, в классе периодических бесконечнозонных функций. Алгебра и анализ. Том 34(2022), No5, с.139-172
А.Б.Хасанов, Т.Г.Хасанов, “Интегрирование нелинейного уравнения Кортевега-де Фриза с нагруженным членом и источником”,Сиб. журн. индустр. матем.,25:2 (2022),127–142
Khasanov, A.B., Tursunov F.R. On the Cauchy Problem for the Three-Dimensional Laplace Equation. Russian Mathematics, 2021, 65(2), pp. 49–64.
Khasanov, A., Hoitmetov U. On Integration of the Loaded mKdV Equation in the Class of Rapidly Decreasing Functions. Bulletin of Irkutsk State University, Series Mathematics, 2021, 38, pp. 19–35.
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, 2021, 47(2), pp. 250–261.
Khasanov, A.B., Matyakubov M.M. Integration of the nonlinear Korteweg–de Vries equation with an additional term. Theoretical and Mathematical Physics(Russian Federation), 2020, 203(2), pp. 596–607.
Mirzaev, O.E., Khasanov, A.B. On families of isospectral Sturm-Liouville boundary value problems. Ufa Mathematical Journal, 2020, 12(2), pp. 28–34.