非线性混合气体方程的可积性求解

doi:10.12677/PM.2022.123048

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非线性混合气体方程的可积性求解
On the Integrability of Nonlinear Mixed Gas Equations

DOI: 10.12677/PM.2022.123048, PDF, HTML, 下载: 227 浏览: 1,682
作者: 加羊杰：青海师范大学民族师范学院数学系，青海西宁
关键词: 玻色-费米混合气体；孤子解；约化摄动法；Bose-Fermi Gas Mixture； Soliton Solution； Reductive Perturbation Technique

摘要: 文章主要对约化摄动法理论进行了深入研究，给出了(1+1)玻色-费米混合超流气体的孤波模型，给出其非线性波方程的解析解，并讨论了孤子的相互作用行为。玻色-费米混合气体中的二维物质波脉冲，包括线性的和非线性的，以及在幺正性体系的限制条件中运用约化摄动法进行计算，得到一个藕合KdV方程，进一步研究和讨论其方程的可积性。

Abstract: In this paper, the theory of reduced perturbation method is well investigated. The solitary wave model of (1+1) Bose-Fermi mixed superfluid gas is given, the analytical solution of its nonlinear wave equation is given, and the interaction behavior of solitons is discussed. A coupled KdV equation is obtained by calculating the two-dimensional matter wave pulses in Bose-Fermi mixture gas, including linear and nonlinear, and by using the reduced perturbation method under the constraint conditions of unitary system. The integrability of the equation is further studied and discussed.

文章引用：加羊杰. 非线性混合气体方程的可积性求解[J]. 理论数学, 2022, 12(3): 434-440. https://doi.org/10.12677/PM.2022.123048

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