B. Deconinck, S.A. Dyachenko, P.M. Lushnikov, A. Semenova,
The dominant instability of near-extreme Stokes waves. The Proceedings of the National Academy of Sciences (PNAS), v. 120 (32) e2308935120 (2023).
(DOI: 10.1073/pnas.2308935120)
(arXiv:2211.05473 PDF)
D.M. Ambrose, P.M. Lushnikov, M. Siegel, and D.A. Silantyev,
Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains, Nonlinearity, v. 37, 025004 (2024).
(DOI: 10.1088/1361-6544/ad140c)
(arXiv:2207.07548 PDF)
A.O. Korotkevich, P.M. Lushnikov, A. Semenova, S.A. Dyachenko,
Superharmonic Instability of Stokes Waves,
Studies in Applied Mathematics (2022).
(DOI: 10.1111/sapm.12535)
(arXiv:2206.00725 PDF)
P.M. Lushnikov, D.A. Silantyev and M. Siegel,
Collapse vs. blow up and global existence in the generalized Constantin-Lax-Majda equation, Journal of Nonlinear Science, v. 31, 82 (2021).
(DOI: 10.1007/s00332-021-09737-x)
(arXiv:2010.01201 PDF)
A.I. Dyachenko, S.A. Dyachenko, P.M. Lushnikov and V.E. Zakharov,
Short branch cut approximation in two-dimensional hydrodynamics with free surface, Proc. Roy. Soc. A, v. 477, 20200811 (2021).
( PDF)DOI: 10.1098/rspa.2020.0811
P.M. Lushnikov and V.E. Zakharov,
Poles and branch cuts in free surface hydrodynamics, Water Waves, v. 3, 251-266 (2021).
( PDF).
DOI: 10.1007/s42286-020-00040-y
A. Semenova, S.A. Dyachenko, A.O. Korotkevich, P.M. Lushnikov,
Comparison of Split-Step and Hamiltonian Integration Methods for Simulation of the Nonlinear Schrödinger Equation,
Journal of Computational Physics, v. 427, 110061 (2021).
( PDF).
DOI: 10.1016/j.jcp.2020.110061
I. Kolokolov, V. Lebedev, P.M. Lushnikov,
Statistical properties of a laser beam propagating in a turbulent medium, Physical Review E, v. 101, 042137 (2020).
( PDF)DOI:10.1103/PhysRevE.101.042137
A.I. Dyachenko, S.A. Dyachenko, P.M. Lushnikov and V.E. Zakharov,
Dynamics of Poles in 2D Hydrodynamics with Free Surface: New
Constants of Motion, Journal of Fluid Mechanics, v. 874, 891-925
(2019).
(arXiv:1809.09584 PDF)DOI:10.1017/jfm.2019.448
A.I. Dyachenko, P.M. Lushnikov and V.E. Zakharov,
Non-Canonical Hamiltonian Structure and Poisson Bracket for 2D Hydrodynamics with Free Surface, Journal of Fluid Mechanics, v. 869, pp. 526-552
(2019).
(arXiv:1711.02841 PDF)DOI: dx.doi.org/10.1017/jfm.2019.219
P.M. Lushnikov and N.M. Zubarev, Exact solutions for nonlinear development of Kelvin-Helmholtz instability for counterflow of superfluid and normal components of Helium II.
Phys. Rev. Lett., v. 120, 204504 (2018).
( PDF)DOI:10.1103/PhysRevLett.120.204504
P.M. Lushnikov and N. Vladimirova, Toward defeating diffraction and randomness for laser beam propagation in turbulent atmosphere.
JETP Lett., v. 108, issue 9, p. 571-576 (2018).
(arXiv:1711.02841 PDF)DOI: 10.1134/S0021364018210026
L.G. Wright, Z.M. Ziegler, P.M. Lushnikov, Z. Zhu, M.A. Eftekhar, D.N. Christodoulides, F.W. Wise, Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial and Outlook.
IEEE Journal of Selected Topics in Quantum Electronics, v. 24, 5100516 (2018).
(arXiv:1708.05324 PDF) DOI: 10.1109/JSTQE.2017.2779749
P.M. Lushnikov, S.A. Dyachenko and D.A. Silantyev, New conformal mapping for adaptive resolving of the complex singularities of Stokes
wave.
Proc. Roy. Soc. A, v. 473, 20170198 (2017).
(arXiv:1703.06343 PDF)
DOI: dx.doi.org/10.1098/rspa.2017.0198
D.A. Silantyev, P.M. Lushnikov and H.A. Rose, Langmuir wave filamentation in the kinetic regime. II. Weak and strong
pumping of nonlinear electron plasma waves as the route to filamentation.
Phys. of Plasmas, v. 24, 042105 (2017).
(PDF)
DOI: 10.1063/1.4979290
D.A. Silantyev, P.M. Lushnikov and H.A. Rose, Langmuir wave filamentation in the kinetic regime. I. Filamentation instability
of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations.
Phys. of Plasmas, v. 24, 042104 (2017).
(PDF)
DOI: 10.1063/1.4979289
P.M. Lushnikov, Structure and location of branch point singularities for Stokes waves on deep water.
Journal of Fluid Mechanics, v. 800, pp. 557-594 (2016).
(PDF)
DOI: 10.1017/jfm.2016.405
S.A. Dyachenko, P.M. Lushnikov, and A.O. Korotkevich, Branch
cuts of Stokes wave on deep water. Part I: Numerical solution and Pade
approximation.
Studies in Applied Mathematics, v. 137, pp. 419-472 (2016). DOI: 10.1111/sapm.12128 (arXiv:1507.02784 PDF)
P.M. Lushnikov and N. Vladimirova, Nonlinear combining of multiple laser beams in Kerr medium.
Optics Express, v. 23, pp. 31120-31125 (2015).
(PDF)
A.O. Korotkevich, P.M. Lushnikov, and H.A. Rose, Beyond the
random phase approximation: Stimulated Brillouin backscatter for finite
laser coherence times.
Phys. of Plasmas, v. 22, 012107 (2015).
(PDF)
DOI: 10.1063/1.4906057
P.M. Lushnikov and N. Vladimirova, Nonlinear combining of laser beams.
Optics Letters, v.39, 3429-3432 (2014).
(PDF)
DOI: 10.1364/OL.39.003429
P.M. Lushnikov, H.A. Rose, D.A. Silantyev, and N. Vladimirova, Vlasov multi-dimensional model dispersion relation.
Phys. of Plasmas, v. 21, 072103 (2014).
(PDF)
DOI: 10.1063/1.4886122
S.I. Dejak, D. Egli, P.M. Lushnikov, and I.M. Sigal. On blowup dynamics in the Keller-Segel model of chemotaxis.
St. Petersburg Mathematical Journal, v. 25,547-574 (2014).
(PDF)
S.A. Dyachenko, P.M. Lushnikov, and A.O. Korotkevich. The complex singularity of a Stokes wave.
JETP Letters, v. 98, 675-679 (2014).
(PDF)
DOI: 10.1134/S0021364013240077
S.A. Dyachenko, P.M. Lushnikov and N. Vladimirova. Logarithmic scaling of the collapse in the critical Keller-Segel equation.
Nonlinearity, v. 26, 3011-3041 (2013).
(PDF) DOI: 10.1088/0951-7715/26/11/3011
P.M. Lushnikov, S.A. Dyachenko and N. Vladimirova. Beyond
leading-order logarithmic scaling in the catastrophic self-focusing of a
laser beam in Kerr media. Physical Review A, v. 88, 013845 (2013).
(PDF) DOI: 10.1103/PhysRevA.88.013845
S.I. Dejak, P.M. Lushnikov, Y.N. Ovchinnikov, and I.M. Sigal. On
Spectra of Linearized Operators for Keller-Segel Models of Chemotaxis.
Physica D, v. 241, 1245-1254 (2012).
(PDF) DOI: 10.1016/j.physd.2012.04.003
P.M. Lushnikov, P. Sulc, and K.S. Turitsyn, Non-Gaussianity in
single-particle tracking: Use of kurtosis to learn the characteristics
of a cage-type potential.
Physical Review E, v. 85, 051905 (2012) (PDF).
DOI: 10.1103/PhysRevE.85.051905
R. Gejji, P.M. Lushnikov, and M. Alber, Macroscopic model of
self-propelled bacteria swarming with regular reversals.
Physical Review E, v. 85, 021903 (2012).
(PDF). DOI: 10.1103/PhysRevE.85.021903
Y. Chung and P.M. Lushnikov, Strong Collapse Turbulence in Quintic Nonlinear Schrodinger Equation.
Physical Review E, v. 84, 036602 (2011) (PDF).
DOI: 10.1103/PhysRevE.84.036602
A.O. Korotkevich, and P.M. Lushnikov, Proof of concept implementation of
the massively parallel algorithm for simulation of dispersion-managed
WDM optical fiber systems.
Optics Letters, v. 36, 1851-1853 (2011). (PDF).
P.M.
Lushnikov and N. Vladimirova. Non-Gaussian Statistics of Multiple Filamentation. Optics Letters v. 35, 1965-1967 (2010).
(PDF)
P.M.
Lushnikov. Collapse and stable self-trapping for Bose-Einstein
condensates with 1/r^b type attractive interatomic interaction
potential.
Physical Review A, v. 82, 023615 (2010).
(PDF)
P.M.
Lushnikov. Critical chemotactic collapse. Physics Letters A, v. 374, 1678-1685 (2010).
(PDF)
P.M.
Lushnikov, N. Chen, and M. Alber. Macroscopic dynamics of biological cells interacting
via chemotaxis and direct contact. Physical Review E, v. 78, p. 061904 (2008).
(PDF)
M. Alber, N. Chen, P.M. Lushnikov, and S.A. Newman. Continuous
macroscopic limit of a discrete stochastic model for interaction of
living cells.
Physical Review Letters, v. 99, p. 168102 (2007).
(PDF)
I. Gabitov, R. Indik, P.M. Lushnikov, L. Mollenauer, and M. Shkarayev.
Twin Families of Bisolitons in Dispersion Managed Systems.
Optics Letters, v. 32, pp. 605-607 (2007).
(PDF)
P.M.
Lushnikov and H.A.Rose. How much laser power can propagate through fusion plasma?
Plasma Physics and Controlled Fusion, v. 48, pp. 1501-1513 (2006).
(PDF)
M. Alber, N. Chen, T. Glimm and P.M. Lushnikov. Multiscale dynamics of biological cells with chemotactic
interactions: from a discrete stochastic model to a continuous
description.
Phys. Rev. E, v.73, p.051901 (2006).
(PDF)
P.M. Lushnikov, and V.E. Zakharov. On optimal Canonical Variables in the Theory of Ideal Fluid with
Free Surface. Physica D, v.203, pp.9-29 (2005).
(PDF)
P.M. Lushnikov. Diffusion of optical pulse in dispersion-shifted randomly birefringent
optical fibers. Optics Communications, v. 245, pp. 187-192 (2005).
(PDF)
P.M.
Lushnikov and H.A.Rose. Instability versus equilibrium propagation of laser beam in
plasma. Physical Review Letters, v.92 (#25), p. 255003 (2004).
(PDF)
P.M.
Lushnikov. Exactly Integrable Dynamics of Interface between Ideal Fluid and Light Viscous
Fluid. Physics Letters A, v.329 (#1-2), pp.49-54 (2004).
(PDF)
M. Chertkov, I. Gabitov, P. Lushnikov, J. Moeser, Z.
Toroczkai. Pinning method of pulse confinement in optical fiber with
random dispersion.
J. of the Optical Society of America B, v.19 (#11), pp. 2538-2550
(2002). (PDF)
I.R. Gabitov and P. M. Lushnikov. Nonlinearity management in
dispersion managed system. Optics Letters, v.27 (#2), pp.113-115 (2002). (PostScript)
(PDF)
P.M. Lushnikov. Dispersion-managed soliton in a strong dispersion
map limit. Optics Letters, v.26 (#20), pp. 1535-1537 (2001). (PostScript)
(PDF)
P.M. Lushnikov, and M. Saffman. Collapse in a forced three dimensional nonlinear Schrodinger equation.
Phys. Rev. E, v. 62 (#4), pp. 5793-5796 (2000). (PostScript)
(PDF)
P.M. Lushnikov. Dispersion-managed soliton in optical fibers with zero average dispersion.
Optics Letters, v. 25 (#16), pp. 1144-1146 (2000). (PostScript)
(PDF)
P.M. Lushnikov. On the boundary of the dispersion-managed soliton
existence. JETP Letters, v. 72 (#3), pp. 111-114 (2000). (PostScript)
(PDF)
P.M. Lushnikov, and A.V. Mamaev. Spontaneous hexagon formation in photorefractive crystal with a single pump
wave. Optics Letters, v. 24 (#21), pp. 1511-1513 (1999). (PostScript)
(PDF)
P.M. Lushnikov. Light propagation in photorefractive crystals: from rings to hexagons.
Nature (Priroda Magazine of the Russian Academy of Science, in Russian), v.999 (#11), p. 29 (1998).
P.M. Lushnikov, P. Lodahl, and M. Saffman. Transverse modulational instability of counterpropagating quasi-phase-matched
beams in a quadratically nonlinear medium.Optics Letters , v. 23(#21) pp. 1650-1652 (1998). (PostScript)
(PDF)
P.M. Lushnikov. Two mechanisms of surface wave generation: Kelvin-Helmholtz and Miles
instabilities Izvestiya, Atmospheric and Oceanic Physics, v. 34, 370-377
(1998). (GZippedPostScript)
(PDF)
P.M. Lushnikov. Hexagonal optical structures in photorefractive crystals with a feedback
mirror JETP, v. 86(#3), 614-627 (1998). (PostScript)
(PDF)
P.M.
Lushnikov. Dynamic criterion for collapse. JETP Letters, v. 62 (#5), pp. 461-467 (1995). (GZiippedPostScript)
(PDF)
E.A. Kuznetsov, and P.M. Lushnikov. Nonlinear theory of the excitation of waves by a wind due to
the Kelvin-Helmholtz instability. JETP v. 81, 332-340 (1995). (GZippedPostScript)
(PDF)
Book Chapters
M. Alber, N. Chen, T. Glimm, and P.M. Lushnikov. Two-dimensional
Multiscale Model of Cell Motion in a Chemotactic Field, pp. 53-76,
In Single-Cell-Based Models in Biology and Medicine,
Series: Mathematics and Biosciences in Interaction.
Eds. A.R.A. Anderson, M.A.J. Chaplain, K.A. Rejniak. Birkhauser Verlag Basel/Switzerland (2007).
(Link).
Other publications
P.M. Lushnikov, Branch cuts of Stokes wave on deep water. Part II:
Structure and location of branch points in infinite set of sheets of
Riemann surface. arXiv:1509.03393(2016)
S.A. Dyachenko, P.M. Lushnikov, and A.O. Korotkevich, Branch
cuts of Stokes wave on deep water. Part I: Numerical solution and Pade
approximation. arXiv:1507.02784 (2015)
A.O. Korotkevich, and P.M. Lushnikov. Nonlinear Waves and Singularities in Optics, Hydrodynamics and Plasmas.
AIP Conf. Proc., v. 1389, p. 684-685 (2011).
(PDF)
S.A. Dyachenko, P.M. Lushnikov and N. Vladimirova. Logarithmic-type Scaling of the Collapse of Keller-Segel Equation.
AIP Conf. Proc., v. 1389, p. 709-712 (2011).
(PDF)
Y. Chung, P.M. Lushnikov, and N. Vladimirova. Collapse Turbulence in Nonlinear Schrodinger Equation.
AIP Conf. Proc., v. 1168, p. 1235-1238 (2009).
(PDF)
I.R. Gabitov, and P.M. Lushnikov. Symposium: Nonlinear Waves and Singularities in Optics, Hydrodynamics and Plasmas.
AIP Conf. Proc., v. 1168, p. 1217-1218 (2009).
(PDF)
J.L. Kline, D.S. Montgomery, H.A. Rose, S.R. Goldman, D.H. Froula, J.S. Ross, R.M. Stevenson, P.M. Lushnikov.
Mitigation of stimulated Raman scattering in hohlraum plasmas.
Journal of Physics: Conf. Series, v. 112, p. 022030 (2008).
(PDF)
P.M.
Lushnikov and H.A.Rose. Collective stimulated Brillouin backscatter.
arXiv:0710.0634 (2007).
P.M. Lushnikov and H.A. Rose. Practical Formula for Laser Intensity at Beam Spray Onset.
Nuclear Weapons Highlights 2007, p. 70, Los Alamos National Laboratory (2007).
(PDF).
P.M. Lushnikov and H.A. Rose. Practical Formula for Laser Intensity at Beam Spray Onset.
LANL report (2006)
(arxiv.org/pdf/physics/0609233).
P.M.
Lushnikov, and A.V. Mamaev. Hexagonal patterns in photorefractive crystals with feedback for scattered
light. Proceedings of "Seventh Topical Meeting on Photorefractive Materials, Effects,
and Devices". Elsinore, Denmark, 1999.
P.M.Lushnikov. Dynamical criterion of a collapse in the nonlinear Schroedinger equation.
Bulletin of the Russian Academy of Sciences. Physics, v. 61, suppl.,
no.1, pp.46-51 (1997).