Zobrazeno 1 - 10
of 624
pro vyhledávání: '"Lerman L"'
We study the stationary Swift--Hohenberg equation $(\Delta + 1)^2 u - \alpha u - \beta u^2 + u^3=0$ in the whole space $\mathbb R^n$, $2\le n \le 7$. We develop and modify the variational approach introduced by Lerman, Naryshkin and Nazarov (2020) an
Externí odkaz:
http://arxiv.org/abs/2404.05066
Autor:
Lerman, L. M., Trifonov, K. N.
We study topological properties of automorphisms of a 6-dimensional torus generated by integer matrices symplectic with respect to either the standard symplectic structure in six-dimensional linear space or a nonstandard symplectic structure given by
Externí odkaz:
http://arxiv.org/abs/2212.05110
Autor:
Grines, V. Z., Lerman, L. M.
We construct new substantive examples of non-autonomous vector fields on 3-dimensional sphere having a simple dynamics but non-trivial topology. The construction is based on two ideas: the theory of diffeomorpisms with wild separatrix embedding (Pixt
Externí odkaz:
http://arxiv.org/abs/2112.00526
Autor:
Lerman, L. M., Trifonov, K. N.
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same level of
Externí odkaz:
http://arxiv.org/abs/2011.03301
Solitons and cavitons (localized solutions with singularities) for the nonlocal Whitham equations are studied. The equation of a fourth order with a parameter in front of fourth derivative for traveling waves is reduced to a reversible Hamiltonian sy
Externí odkaz:
http://arxiv.org/abs/2006.03958
Autor:
Lerman, L. M., Trifonov, K. N.
We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a foliation generated by unstable leaves of the automorphism. There two
Externí odkaz:
http://arxiv.org/abs/2001.10727
We study entire bounded solutions to the equation $\Delta u - u + u^3 = 0$ in $\mathbb R^2$. Our approach is purely variational and is based on concentration arguments and symmetry considerations. This method allows us to construct in a unified way s
Externí odkaz:
http://arxiv.org/abs/1811.03143
Autor:
Lerman, L., Yakovlev, E.
A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold $M$ and the dynamics of Hamiltonian systems. It is shown that for a given divergence f
Externí odkaz:
http://arxiv.org/abs/1804.10375
Autor:
Lerman, L. M., Gubina, E. V.
We study a class of scalar differential equations on the circle $S^1$. This class is characterized mainly by the property that any solution of such an equation possesses exponential dichotomy both on the semi-axes $\R_+$ and $\R_+$. Also we impose so
Externí odkaz:
http://arxiv.org/abs/1801.10336
Publikováno v:
In Communications in Nonlinear Science and Numerical Simulation February 2021 93
