12 citations · 34 across the 10 of their papers we have counts for
10 papers
Evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theory
L. F. Calazans de Brito, A. Gammal, A. M. Kamchatnov
In this work, we develop, in the Gurevich-Pitaevskii framework, an analytic theory for the evolution of localized pulses in the defocusing modified Korteweg-de Vries equation theor…
Dynamics of ring solitons in an expanding cloud of a Bose-Einstein condensate
A. M. Kamchatnov, B. I. Suleimanov, E. N. Tsoy
In this paper, we derive equations for the dynamics of ring dark solitons in an expanding cloud of a two-dimensional Bose-Einstein condensate. Assuming that the soliton's width is…
Asymptotic integrability of nonlinear wave equations
A. M. Kamchatnov
We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high…
Propagation of dark solitons of DNLS equation along a large-scale background
A. M. Kamchatnov, D. V. Shaykin
We study dynamics of dark solitons in the theory of the DNLS equation by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition…
Hamilton theory of NLS equation soliton motion
A. M. Kamchatnov
We suggest the method of derivation of Hamilton equations which describe the motion of solitons along non-uniform and time dependent large-scale background in case of wave dynamics…
Quasiclassical integrability condition in AKNS scheme
A. M. Kamchatnov, D. V. Shaykin
In this paper, we study the condition of quasiclassical integrability of soliton equations. This condition states that the Hamiltonian structure of equations, which govern propagat…
Propagation of instability fronts in modulationally unstable systems
A. M. Kamchatnov, D. V. Shaykin
We study evolution of pulses propagating through focusing nonlinear media. Small disturbance on the smooth initial non-uniform background leads to formation of the region of strong…
Evolution of initial discontinuities in the DNLS equation theory
A. M. Kamchatnov
We present the full classification of wave patterns evolving from an initial step-like discontinuity for arbitrary choice of boundary conditions at the discontinuity location in th…
On periodic solutions and their modulations for the Manakov system
A. M. Kamchatnov
Periodic solutions of the Manakov system are studied with the aim to establish links between recent results of Wright (Physica D 2013 {\bf 264} 1) and Kamchatnov (EPL 2013 \textbf{…
Kinetic equation for a soliton gas and its hydrodynamic reductions
G. A. El, A. M. Kamchatnov, M. V. Pavlov +1
We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between soli…