On Complex-Valued Solutions of the General Loaded Korteweg-de Vries Equation with a Source

被引：4

作者：

Khasanov, A. B. ^{[1
]}

Hoitmetov, U. A. ^{[2
,3
]}

机构：

[1] Samarkand State Univ, Samarkand 140104, Uzbekistan

[2] Uzbek Acad Sci, Romanovskii Inst Math, Khwarazm Branch, Urgench, Uzbekistan

[3] Urgench State Univ, Urgench 220100, Uzbekistan

来源：

DIFFERENTIAL EQUATIONS | 2022年 / 58卷 / 03期

关键词：

INTEGRATION;

D O I：

10.1134/S0012266122030089

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the inverse scattering method, we derive the evolution of the scattering data of a nonself-adjoint Sturm-Liouville operator whose potential is a solution of the general loaded Korteweg-de Vries equation with a self-consistent source in the class of rapidly decaying complex-valued functions. An example is given to illustrate the application of the results obtained.

引用

页码：381 / 391

页数：11

共 50 条

[1] On Complex-Valued Solutions of the General Loaded Korteweg–de Vries Equation with a Source
A. B. Khasanov
U. A. Hoitmetov
Differential Equations, 2022, 58 : 381 - 391
[2] Integration of the General Loaded Korteweg-de Vries Equation with an Integral Type Source in the Class of Rapidly Decreasing Complex-Valued Functions
Khasanov, A. B.
Hoitmetov, U. A.
RUSSIAN MATHEMATICS, 2021, 65 (07) : 43 - 57
[3] INTEGRATION OF THE LOADED GENERAL KORTEWEG-DE VRIES EQUATION IN TNE CLASS OF RAPIDLY DECREASING COMPLEX-VALUED FUNCTIONS
Hoitmetov, Umid Azadovich
EURASIAN MATHEMATICAL JOURNAL, 2022, 13 (02): : 43 - 54
[4] Integration of the General Loaded Korteweg–de Vries Equation with an Integral Type Source in the Class of Rapidly Decreasing Complex-Valued Functions
A. B. Khasanov
U. A. Hoitmetov
Russian Mathematics, 2021, 65 : 43 - 57
[5] Explicit complex-valued solutions of the Korteweg-de Vries equation on the half-line and on the whole-line
Vu, PL
ACTA APPLICANDAE MATHEMATICAE, 1997, 49 (02) : 107 - 149
[6] Quasiperiodic solutions of the Korteweg-de Vries equation
Yu. N. Zaiko
Technical Physics Letters, 2002, 28 : 235 - 236
[7] Computability of solutions of the Korteweg-de Vries equation
Gay, W
Zhang, BY
Zhong, N
MATHEMATICAL LOGIC QUARTERLY, 2001, 47 (01) : 93 - 110
[8] On the singular solutions of the Korteweg-de Vries equation
S. I. Pokhozhaev
Mathematical Notes, 2010, 88 : 741 - 747
[9] Solutions to the modified Korteweg-de Vries equation
Zhang, Da-Jun
Zhao, Song-Lin
Sun, Ying-Ying
Zhou, Jing
REVIEWS IN MATHEMATICAL PHYSICS, 2014, 26 (07)
[10] On the general Korteweg-de Vries equation with a source in the class of steplike functions
Khasanov, AB
Urazboev, GU
DOKLADY MATHEMATICS, 2004, 70 (01) : 512 - 515

← 1 2 3 4 5 →