Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method

被引：6

作者：

Ene, Remus-Daniel ^{[1
]}

Pop, Nicolina ^{[2
]}

Lapadat, Marioara ^{[1
]}

Dungan, Luisa ^{[3
]}

机构：

[1] Politehn Univ Timisoara, Dept Math, 2 Victoria Sq, Timisoara 300006, Romania

[2] Politehn Univ Timisoara, Dept Phys Foundat Engn, 2 Vasile Parvan Blvd, Timisoara 300223, Romania

[3] Politehn Univ Timisoara, Mech Machines Equipment & Transports Dept, Timisoara 300222, Romania

来源：

MATHEMATICS | 2022年 / 10卷 / 21期

关键词：

Maxwell-Bloch equations; Hamilton-Poisson realization; periodical orbits; symmetries; optimal homotopy asymptotic method; SYMMETRIES; INTEGRABILITY; REALIZATIONS; STABILITY; SYSTEM;

D O I：

10.3390/math10214118

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper emphasizes some geometrical properties of the Maxwell-Bloch equations. Based on these properties, the closed-form solutions of their equations are established. Thus, the Maxwell-Bloch equations are reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions were built using the optimal homotopy asymptotic method (OHAM). These represent the epsilon-approximate OHAM solutions. A good agreement between the analytical and corresponding numerical results was found. The accuracy of the obtained results is validated through the representative figures. This procedure is suitable to be applied for dynamical systems with certain geometrical properties.

引用

页数：13

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