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All articles by
Kamchatnov A. M. | Kamchatnov Anatoly M. | Kamchatnov A. | Kamchatnov Anatoly

A | A Gustavo Bruzual | A Dang Quang | A Krishna Chaitanya | A Lazarian | A Germina K | A M. | A Pranav | A Antony Franklin | A Azeef Muhammed P

M Rajesh Kumar | M Ajith K. | M | M Anand Kumar | M Malaya Kumar Biswal | M Gurunath Reddy | M J. L. Lucio | M Rahul | M Sasikumar | M Shyam Mohan

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Theory of quasi-simple dispersive shock waves and number of solitons evolved from a nonlinear pulse

Kamchatnov A. M.
22 Aug 2020 nlin.PS arxiv.org/abs/2008.09786

The theory of motion of edges of dispersive shock waves generated after wave breaking of simple waves is developed. It is shown that this motion obeys Hamiltonian mechanics complemented by a Hopf-like equation for evolution of the background flow that interacts with edge wave packets or edge solitons. A conjecture about existence of a certain symmetry between equations for the small-amplitude and soliton edges is formulated. In case of localized simple wave pulses propagating through a quiescent medium this theory provided a new approach to derivation of an asymptotic formula for the number of solitons produced eventually from such a pulse.

Plasma slab expansion into vacuum

Ivanov S. K., Kamchatnov A. M.
10 Jul 2020 nlin.PS physics.flu-dyn physics.plasm-ph arxiv.org/abs/2007.05359

The problem of collisionless plasma slab expansion into vacuum is solved within a two-temperature hydrodynamic approximation in the dispersionless limit of zero Debye radius. In the framework of such an approach, the solution by the Riemann method provides quite accurate description of the whole process of plasma dynamics. It is shown that the dispersionless approximation agrees very well with exact numerical solution of the full system of plasma hydrodynamic equations.

Dispersionless evolution of inviscid nonlinear pulses

Isoard M., Pavloff N., Kamchatnov A. M.
10 Dec 2019 nlin.PS cond-mat.quant-gas physics.optics arxiv.org/abs/1912.04559

We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well with exact results and numerical simulations for other systems. We also provide a simple and accurate determination of the wave breaking time for typical initial conditions.

Landau-Khalatnikov problem in relativistic hydrodynamics

Kamchatnov A. M.
09 Jun 2019 nlin.PS arxiv.org/abs/1906.03596

An alternative approach to solving the Landau-Khalatnikov problem on one-dimensional stage of expansion of hot hadronic matter created in collisions of high-energy particles or nuclei is suggested. Solving the relativistic hydrodynamics equations by the Riemann method yields a representation for Khalatnikov's potential which satisfies explicitly the condition of symmetry of the matter flow with respect to reflection in the central plane of the initial distribution of matter. New exact relationships are obtained for evolution of the density of energy in the center of the distribution and for laws of motion of boundaries between the general solution and the rarefaction waves. The rapidity distributions are derived in the Landau approximation with account of the pre-exponential factor.

Evolution of intensive light pulses in a nonlinear medium with the Raman effect

Ivanov S. K., Kamchatnov A. M.
11 Apr 2019 nlin.PS arxiv.org/abs/1904.05784

In this paper, we study the evolution of intensive light pulses in nonlinear single-mode fibers. The dynamics of light in such fibers is described by the nonlinear Schr\"odinger equation with the Raman term, due to stimulated Raman self-scattering. It is shown that dispersive shock waves are formed during the evolution of sufficiently intensive pulses. In this case, the situation is much richer than for the nonlinear Schr\"odinger equation with Kerr nonlinearity only. The Whitham equations are obtained under the assumption that the Raman term can be considered as a small perturbation. These equations describe slow evolution of dispersive shock waves. It is shown that if one takes into account the Raman effect, then dispersive shock waves can asymptotically acquire a stationary profile. The analytical theory is confirmed by numerical calculations.

Evolution of wave pulses in fully nonlinear shallow-water theory

Ivanov S. K., Kamchatnov A. M.
04 Mar 2019 nlin.PS arxiv.org/abs/1903.01667

We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the dispersive shock edges is studied within the Whitham theory of modulations. Simple analytical formulas are obtained for asymptotic stage of evolution of initially localized pulses. Analytical results are confirmed by exact numerical solutions of the fully nonlinear shallow-water equations.

Short-distance propagation of nonlinear optical pulses

Isoard M., Kamchatnov A. M., Pavloff N.
28 Feb 2019 nlin.PS physics.flu-dyn physics.optics arxiv.org/abs/1903.00344

We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a defocusing nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be described within a nondispersive approximation by means of Riemann's approach. The theoretical results are in excellent agreement with numerical simulations.

Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material

Isoard M., Kamchatnov A. M., Pavloff N.
19 Feb 2019 nlin.PS physics.flu-dyn arxiv.org/abs/1902.06975

We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be described within a nondispersive approximation by means of Riemann's approach. For larger distances, wave breaking occurs, leading to the formation of dispersive shocks at both ends of the pulse. We describe this phenomenon within Whitham modulation theory, which yields an excellent agreement with numerical simulations. Our analytic approach makes it possible to extract the leading asymptotic behavior of the parameters of the shock.

Wave Breaking in Dispersive Fluid Dynamics of the Bose-Einstein Condensate

Kamchatnov A. M.
27 Dec 2018 nlin.PS arxiv.org/abs/1812.10683

The problem of wave breaking during its propagation in the Bose-Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form $(-x)^{1/n}$. The evolution of the wave is described by the Gross-Pitaevskii equation so that a dispersive shock wave is formed as a result of breaking; this wave can be represented using the Gurevich-Pitaevskii approach as a modulated periodic solution to the Gross-Pitaevskii equation, and the evolution of the modulation parameters is described by the Whitham equations obtained by averaging the conservation laws over fast oscillations in the wave. The solution to the Whitham modulation equations is obtained in closed form for $n = 2,3$, and the velocities of the dispersion shock wave edges for asymptotically long evolution times are determined for arbitrary integer values $n > 1$. The problem considered here can be applied for describing the generation of dispersion shock waves observed in experiments with the Bose-Einstein condensate.

Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons revisited: Whitham method

Isoard M., Kamchatnov A. M., Pavloff N.
18 Oct 2018 nlin.PS physics.flu-dyn arxiv.org/abs/1810.07952

We consider the long-time evolution of pulses in the Korteweg-de Vries equation theory for initial distributions which produce no soliton, but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach based on Whitham modulation theory makes it possible to obtain an analytic description of the structure and to describe its self-similar behavior near the soliton edge of the shock. The results are compared with numerical simulations.