TY - JOUR
AU - Сагидуллаева, Ж.М.
PY - 2022/07/04
Y2 - 2024/05/21
TI - On the gauge equivalence of the two-layer M-XCIX equation and the two-component Schr¨odinger-Maxwell-Bloch equation
JF - BULLETIN OF THE L.N. GUMILYOV EURASIAN NATIONAL UNIVERSITY. PHYSICS. ASTRONOMY SERIES
JA - physast
VL - 124
IS - 3
SE -
DO - 10.32523/2616-6836-2018-124-3-41-46
UR - https://bulphysast.enu.kz/index.php/physast/article/view/163
SP - 41-46
AB - <p>The interest in integrable systems increased with the discovery in the late 1960s of the Inverse scattering problem method, which arose as a result of investigations in plasma physics. M.D. Kruskal and N. Zabusky, investigating the Korteweg-de Vries equation, found by numerical simulation that its exact soliton solutions collide resiliently, which is not typical for linear waves. This served as a new impetus to the development of various methods for solving nonlinear evolution equations, as well as solitons and solutions associated with them. The gauge equivalence of the two-component Schr¨odinger-Maxwell-Bloch equation, the Γ -spin system and the integrable two-layer spin system, the so-called two-layer Myrzakulov-XCIX equation, is proved in this work. These systems of equations are integrable and admit Lax representations. Complete formsfor the Γ -spin system with a self-consistent potential and the two-layer spin system with potentials are established. The Myrzakulov-XCIX equation is the soliton equation describing nonlinear magnetization processes in multilayer ferromagnets.</p>
ER -