A Cauchy Problem for the Boussinesq-Love Equation with the Bessel Operator

被引：0

作者：

Karimov, Sh. ^{[1
]}

Oripov, Sh. ^{[1
]}

机构：

[1] Fergana State Univ, Fergana, Uzbekistan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2024年 / 45卷 / 09期

关键词：

Cauchy problem; Boussinesq-Love equations; Bessel operator; transmutation operator; Riemann function;

D O I：

10.1134/S1995080224605113

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The article investigates the Cauchy problem for the Boussinesq-Love equation with the Bessel operator. The problem is solved using the Riemann method. The Erdelyi-Kober transmutation operator is applied to construct the Riemann function. The Riemann function for this equation is derived, which is expressed in terms of hypergeometric functions. In particular, the Riemann function for the one-dimensional Boussinesq-Love equation is obtained. Based on the Riemann function, an explicit formula for the solution to the Cauchy problem is found.

引用

页码：4520 / 4533

页数：14

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