The Cauchy Problem for the Nonlinear Complex Modified Korteweg-de Vries Equation with Additional Terms in the Class of Periodic Infinite-Gap Functions

被引：0
|
作者：
Khasanov, A. B. [1 ,2 ]
Khasanov, T. G. [3 ]
机构：
[1] Samarkand State Univ, Samarkand, Uzbekistan
[2] VI Romanovskii Inst Math, Samarkand Div, Samarkand, Uzbekistan
[3] Urgench State Univ, Urgench, Uzbekistan
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2024年 / 65卷 / 04期
关键词：
complex modified Korteweg-de Vries equation; Dirac operator; spectral data; system of Dubrovin differential equations; trace formulas; 517.957; SELF-CONSISTENT SOURCE; SINE-GORDON EQUATION; INVERSE PROBLEM; SOLITON-SOLUTIONS; MULTISOLITON SOLUTIONS; SCHRODINGER-EQUATION; INSTABILITY ZONES; INTEGRATION; ASYMPTOTICS; SCATTERING;
D O I：
10.1134/S0037446624040128
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We use the inverse spectral problem method for integrating the nonlinear complex modified Korteweg-de Vries equation (cmKdV) with additional terms in the class of periodic infinite-gap functions. Also, we deduce the evolution of the spectral data of the periodic Dirac operator whose coefficient is a solution to cmKdV. We prove that the Cauchy problem is solvable for an infinite system of Dubrovin differential equations in the class of six times continuously differentiable periodic infinite-gap functions. Moreover, we establish the solvability of the Cauchy problem for cmKdV with additional terms in the class of six times continuously differentiable periodic infinite-gap functions.
引用
收藏
页码：846 / 868
页数：23
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