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,   
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

参考文献

[1] Fleck Jr., J.A., Morris, J.R. and Feit, M.D. (1976) Time-Dependent Propagation of High Energy Laser Beams through the Atmosphere. Applied Physics, 10, 129-160.[CrossRef] 
[2] Chowdhury, A.R. and Roy, T. (1979) Prolongation Structure and Inverse Scattering Formalism for Supersymmetric Sine-Gordon Equation in Ordinary Space Time Variable. Progress of Theoretical Physics, 62, 1790-1791.[CrossRef] 
[3] Dodd, R.K. and Fordy, A.P. (1983) The Prolongation Structures of Quasi-Polynomial Flows. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 385, 389-429. [Google Scholar] [CrossRef] 
[4] Yang, Y., Geng, L.M. and Cheng, J.P. (2021) CKP Hierarchy and Free Bosons. Journal of Mathematical Physics, 62, 8-21. [Google Scholar] [CrossRef] 
[5] Kalkanh, A. (1987) Prolongation Structure and Painleve Property of the Gu¨rses-Nutku Equations. International Journal of Theoretical Physics, 26, 1085-1092. [Google Scholar] [CrossRef] 
[6] Finley III, J.D. (1996) The Robinson-Trautman Type III Prolongation Structure Contains K2. Communications in Mathematical Physics, 178, 375-390. [Google Scholar] [CrossRef] 
[7] Zhao, W.Z., Bai, Y.Q. andWu, K. (2006) Generalized Inhomogeneous Heisenberg Ferromagnet Model and Generalized Nonlinear Schrodinger Equation. Physics Letters A, 3, 52-64.
[8] Das, C. and Chowdhury, A. (2001) On the Prolongation Structure and Integrability of HNLS Equation. Chaos, Solitons and Fractals, 12, 2081-2086.[CrossRef] 
[9] Alfinito, E., Grassi, V., Leo, R.A., Profilo, G. and Soliani, G. (1998) Equations of the Reaction- Diffusion Type with a Loop Algebra Structure. Inverse Problems, 14, 1387-1401.[CrossRef] 
[10] Gilson, C.R., Nimmo, J. and Ohta, Y. (2012) Quasideterminant Solutions of a Non-Abelian Hirota-Miwa Equation. Journal of Physics A: Mathematical and Theoretical, 39, 5053-5065.[CrossRef] 
[11] Ito, M. (1982) Symmetries and Conservation Laws of a Coupled Nonlinear Wave Equation. Physics Letters A, 91, 335-338. [Google Scholar] [CrossRef] 
[12] Cao, C., Geng, X.G. and Wu, Y.T. (1999) From the Special 2 + 1 Toda Lattice to the Kadomtsev-Petviashvili Equation. Journal of Physics A: General Physics, 32, 8059-8078.[CrossRef] 
[13] Adhikari, S.K. and Salasnich, L (2008) Superuid Bose-Fermi Mixture from Weak Coupling to Unitarity. Physical Review A, 78, Article ID: 043616.[CrossRef] 
[14] 李妹敏, 斯仁道尔吉. 非线性差分-微分方程的Jacobi椭圆函数解[J]. 西 师范大学学报(自然科学版), 2007, 43(4): 41-45.
[15] 姬利娜, 冯玛. 带有热源项的非线性扩散方程的精确解[J]. 纯粹数学与应用数学, 2010, 26(5):725-727.
[16] 吕毅斌, 罗志强. 多重点源自由面波运功规律数值模拟[J]. 纯粹数学与应用数学, 2020, 1(2):94-104.

为你推荐