arXiv subjects

Zh. Myrzakulova

Publications and source records attributed to Zh. Myrzakulova.

3 recordsLinked to original sources

arXiv2026

Integrable Zhaidary equations: reductions and gauge equivalence

The present work addresses the study and characterization of the integrability of some generalized spin systems (ISS) in 1+1 dimensions. Lax representations for these ISS are successfully obtained. The gauge equivalent counterparts of these integrable ISS are presented. Finally, we consider Zhanbota transcendents and some integrable Zhanbota equations. In particular, the gauge equivalence between some Zhanbota equations and the six Painleve equations is established.

nlin.SI↗

arXiv2025

Integrability, geometry and wave solutions of some Kairat equations

In this paper, we study some Kairat equations. The relation between the motion of curves and Kairat equations is established. The geometrical equivalence between the Kairat-I equation and the Kairat-II equation is proved. We also proves that these equations is gauge equivalent to each other. Three types traveling wave solutions of the Kairat-II equation as well as its some integrals of motion are found. The techniques used in this paper can be adopted to study other integrable spin systems and nonlinear models. In particular, using these methods we study some Zhanbota equations.

nlin.SI↗

arXiv2022

Integrable motion of anisotropic space curves and surfaces induced by the Landau-Lifshitz equation

In this paper, we have studied the geometrical formulation of the Landau-Lifshitz equation (LLE) and established its geometrical equivalent counterpart as some generalized nonlinear Schrödinger equation. When the anisotropy vanishes, from this result follows the well-known results corresponding for the isotropic case, i.e. to the Heisenberg ferromagnet equation and the focusing nonlinear Schrödinger equation. The relations between the LLE and the differential geometry of space curves in the local and nonlocal cases are studied. Using the well-known Sym-Tafel formula, the soliton surfaces induced by the LLE are briefly considered.

nlin.SI↗