27 citations · 74 across the 9 of their papers we have counts for
9 papers
The vector form of Kundu-Eckhaus equation and its simplest solutions
Aleksandr O. Smirnov, Aleksandra A. Caplieva
In our work a hierarchy of integrable vector nonlinear differential equations depending on the functional parameter is constructed using a monodromy matrix. The first equation…
Fundamental Analytic Solutions for the Kulish-Sklyanin Model with Constant Boundary Conditions
Vladimir S. Gerdjikov, Aleksandr O. Smirnov
In the present paper we analyze the construction of fundamental analytic solutions (FAS) for the generalized Kulish-Sklyanin models (KSM) for vanishing (VBC) and constant boundary…
Generalized invariant manifolds for integrable equations and their applications
I. T. Habibullin, A. R. Khakimova, A. O. Smirnov
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well kn…
Recursion operators and the hierarchies of MKdV equations related to , and Kac-Moody algebras
V. S. Gerdjikov, A. A. Stefanov, I. D. Iliev +4
We constructed the three nonequivalent gradings in the algebra . The first one is the standard one obtained with the Coxeter automorphism $C_1=S_{α_2} S_{α_1}S_{α…
Spectral curves for the rogue waves
Aleksandr O. Smirnov, Vladimir B. Matveev, Yury A. Gusman +1
Here we find the spectral curves, corresponding to the known rational or quasi-rational solutions of AKNS hierarchy equations, ultimately connected with the modeling of the rogue w…
Some comments on continuous symmetries of AKNS hierarchy equations and their solutions
A. O. Smirnov, V. B. Matveev
We show that a well known for NLS equation scaling invariance and Galilean invariance property of its solutions can be extended with appropriate modifications to the whole AKNS hie…
Three-Phase Freak Waves
Aleksandr O. Smirnov, Sergei G. Matveenko, Sergei K. Semenov +1
In the article, we describe three-phase finite-gap solutions of the focusing nonlinear Schrödinger equation and Kadomtsev-Petviashvili and Hirota equations that exhibit the behavio…
On a periodic solution of the focusing nonlinear Schrödinger equation
A. O. Smirnov, E. G. Semenova, V. Zinger +1
A periodic two-phase algebro-geometric solution of the focusing nonlinear Schrödinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solu…
On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation
K. R. Khusnutdinova, C. Klein, V. B. Matveev +1
There exist two versions of the Kadomtsev-Petviashvili equation, related to the Cartesian and cylindrical geometries of the waves. In this paper we derive and study a new version,…