4.
E. L. Aero, S. A. Vakulenko, Asymptotical behaviour of solutions
for a strongly nonlinear model of a crystal lattice
Teor. Matem. Fiz., T. 142, N3, 2005.
5.
S. Vakulenko and S. Genieys, Patterning by genetic networks,
Mathematical Methods in Applied Sciences, V29, (2005) pp. 173 190.GENE_N~1.PS
6.
S. Vakulenko, D. Grigoriev, Algorithms and complexity
in biological pattern formation problems,
Annales of Pure and Applied Logic (in print, 2006)
7.
S.A. Vakulenko, D. Yu. Grigoriev,
Evoluiton in random
environment and structural stability, Zapiski seminarov POMIRAN,
V. 325, (2005), p.28 –60 VAGR2.PS
[8]
S.A. Vakulenko,
An Analytical Approach to
Convective Reaction Fronts,
Asymptotical Analysis, 2003.
[9]
{ S. A. Vakulenko} and V. Volpert,
{ New effects in propagation of waves}
{for reaction-diffusion systems},
Asymptotical Analysis, 2003.
[10]
A. K. Abramian, D. A. Indeitzev
and
S. A. Vakulenko,
Wave Localization in Hydroelastic Systems,
Flow, Turbulence and Combustion {\bf 61}: 1-20, 1999.
[11]
S. A. Vakulenko,
Computational capacities of the time reccurent
neural networks, Journal Phys. A, Math. Gen.
{\bf 35}, pp. 2539-2554, 2002.A21102.PDF
[12]
A. K. Abramian and { S. A. Vakulenko},
Dissipative and Hamiltonian systems with chaotic
behaviour: an analytical approach,
Theoretical and Mathem. Physics, {\bf 130}(2): 244-254
(2002).HYPRON2.PS
[13] Vakulenko, S.; Volpert, V. Generalized travelling waves for
perturbed monotone reaction-diffusion systems. Nonlinear Anal. 46 (2001),
no. 6, Ser. A: Theory Methods, 757--776.
[14] Vakulenko, S. A. Dissipative systems generating any
structurally stable chaos.
Adv. Differential Equations 5 (2000), no. 7-9, 1139--1178.
[15] Gordon, P. V.; Vakulenko, S. A. Merging and
interacting wave fronts for reaction-diffusion equations.
Arch. Mech. (Arch. Mech. Stos.) 51 (1999), no. 5, 547--558.
[16] Vakulenko, S. A.; Gordon, P. V.
Neural networks with prescribed large time behaviour.
J. Phys. A. Math. Gen. 31 (1998), no. 47, 9555--9570.
[17] Vakulenko, S. A.; Gordon, P. V. Propagation and
scattering of kinks in a nonhomogeneous nonlinear medium. (Russian)
Teoret. Mat. Fiz. 112 (1997), no. 3, 384--394; translation
in Theoret. and Math. Phys. 112 (1997), no. 3, 1104--1112 (1998)
[18] Aero E. L., Vakulenko, S. A.
Kinematics of nonlinear oriented deformations in
nematic liquid crystals in a homogeneous magnetic field. (Russian)
Prikl. Mat. Mekh. 61 (1997),
no. 3, 479--490; translation in J. Appl. Math. Mech. 61 (1997), no. 3,
463--473.
[19] S. Frenkel, B. Stuhn, { S. Vakulenko}, A. Vilesov,
Kinetics of superstructure formation, J. of Chemical Phys.
(1997), 106, pp. 3412-3416.
[20] Gordon, P. V.; Vakulenko, S. A.
Periodic kinks in reaction-diffusion systems.
J. Phys. A. Math. Gen. 31 (1998), no. 3, L67--L70.
[21] Vakulenko, S. A.; Molotkov, I. A.
The initial stage of evolution of displacement fronts in a nonlinear
filtration problem. (Russian) Prikl. Mat. Mekh. 61 (1997), no. 1, 108--114;
translation in J. Appl. Math. Mech. 61 (1997),
no. 1, 103--109
[22]
Vakulenko, S. A. Reaction-diffusion systems with prescribed
large time behaviour. Ann. Inst. H. Poincare
V. 66 (1997), no. 4, 373--410.
[23] Bessonov, N. M.; Vakulenko, S. A.
Connected kink states in nonhomogeneous nonlinear media. (Russian)
Teoret. Mat. Fiz. 107 (1996), no. 1, 115--128; translation in Theoret.
and Math. Phys. 107 (1996), no. 1, 511--522.
[24] Vakulenko, S. A. A system of coupled oscillators
can have arbitrary prescribed attractors. J. Phys. A 27 (1994), no. 7,
2335--2349.
[25] Vakulenko, S. A. The oscillating wave fronts.
Nonlinear Anal. 19 (1992), no. 11, 1033--1046.
[26] Molotkov, I. A.; Vakulenko, S. A.
Autowave propagation for general reaction diffusion systems.
Wave Motion 17 (1993), no. 3, 255-266.
[27] Vakulenko, S. A. Justification of asymptotic solutions for
one-dimensional nonlinear parabolic equations. (Russian)
Mat. Zametki 52 (1992), no. 3, 10--16, 157; translation in
Math. Notes 52 (1992), no. 3-4, 875--880
[28] Vakulenko, S. A. Existence of chemical waves with a
complex motion of the front. (Russian) Zh. Vychisl. Mat. i Mat. Fiz.
31 (1991), no. 5, 735--744; translation in Comput.
Math. Math. Phys. 31 (1991), no. 5, 68--76 (1992)
[29] Aero E. L., { Vakulenko S. A.} and Vilesov A. D.
Kinetic theory
of macrophase separation in block copolymers, Journal de Physique
France 51, 1990, p. 2205 -2226.
[30] Vakulenko, S. A.
The dynamic Whitham principle for parabolic equations and its justification.
(Russian) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 179
(1989), Mat. Vopr. Teor. Rasprostr. Voln. 19, 45, 46--51, 188;
translation in J. Soviet Math. 57 (1991), no. 3, 3093--3096
[31] Vakulenko, S. A.
A variational principle for nonlinear concentrated waves. (Russian)
Prikl. Mat. Mekh. 53 (1989), no. 4, 636--641;
translation in J. Appl. Math. Mech. 53 (1989),
no. 4, 495--500 (1990)
[32] Molotkov, I. A.; Vakulenko, S. A.
Wave beams in an inhomogeneous medium with saturated nonlinearity.
Wave Motion 10 (1988), no. 4, 349--354.
[34] Vakulenko, S. A.; Molotkov, I. A.
Waves in a layered nonlinear medium. (Russian) Vestnik Leningrad.
Univ. Fiz. Khim. 1987, vyp. 2, 21--27, 134.
[35] Vakulenko, S. A.; Molotkov, I. A.
Stationary wave beams in a strongly nonlinear three-dimensional
inhomogeneous medium. (Russian) Mathematical questions in the theory of
wave propagation, No. 15. Zap. Nauchn. Sem. Leningrad.
Otdel. Mat. Inst. Steklov. (LOMI) 148 (1985), 52--60, 191.
[36]
Vakulenko, S. A. Formal-asymptotic integration of a class of weakly
nonlinear \
infinite-dimensional Hamiltonian systems. (Russian)
Mathematical questions in the theory of
wave propagation, No. 15. Zap. Nauchn. Sem. Leningrad.
Otdel. Mat. Inst. Steklov. (LOMI) 148 (1985), 42--51, 191.
[37]
Molotkov, I. A.; Vakulenko, S. A.
Evolution of a wave beam in an inhomogeneous and strongly nonlinear medium.
(Russian) Vestnik Leningrad. Univ. Fiz. Khim. 1985, vyp. 2,
10--15, 122.
[38] Vakulenko, S. A.
Construction of asymptotic solutions for weakly
nonlinear Hamiltonian systems. (Russian)
Mathematical questions in the theory of wave propagation, 14.
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 140 (1984),
36--40. 35C20
[39] Vakulenko, S. A.
Justification of an asymptotic formula for solutions of a
perturbed Klein-Fock-Gordon equation. (Russian)
Mathematical questions in the theory of wave
propagation, 11. Zap. Nauchn. Sem. Leningrad.
Otdel. Mat. Inst. Steklov. (LOMI) 104 (1981), 84--92, 236--237.
[40]
Molotkov, I. A.; Vakulenko, S. A. Nonlinear longitudinal waves in
inhomogeneous rods. (Russian) Interference waves in layered media,
I. Zap. Nauchn. Sem. Leningrad. Otdel.
Mat. Inst. Steklov. (LOMI) 99 (1980), 64--73, 158.
[41] Vakulenko, S. A.
The effect of perturbation on solutions of some nonlinear equations.
(Russian) Mathematical questions in the theory of wave propagation, 10.
Zap. Nauchn.
Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 89 (1979), 91--96,
292--293.
[42] Vakulenko, S. A. The solutions of nonlinear equations
concentrated near curves on a plane. (Russian)
Mathematical questions in the theory of wave propagation, 10. Zap.
Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 89 (1979),
84--90, 292.
[43] Bogdanov, A. V.; Vakulenko, S. A.; Strel'chenya,
V. M. Propagation of perturbations in nonlinear media with dispersion and
dissipation. (Russian) Chisl. Metody Mekh.
Sploshn. Sredy 11 (1980), no. 3, Modeli Sredy, 18--26.
[44] Vakulenko, Serge Existence of RuelleTakens transition to chaos for some evolution equations.
C. R. Acad. Sci. Paris S\`er. I Math. 316 (1993), no. 10, 1015--1018.
[45] Vakulenko, S. A.; Maslov, V. P.; Molotkov, I. A.;
Shafarevich, A. I. Asymptotic solutions of the Hartree equation
that are concentrated, as $h\to 0$, in a small neighborhood of a
curve. (Russian) Dokl. Akad. Nauk 345 (1995), no. 6, 743--745.
[46] Vakulenko, Serge Neural networks and
reaction-diffusion systems with prescribed dynamics. C. R. Acad. Sci.
Paris S\'er. I Math. 324 (1997), no. 5, 509--513.
[46b] Vakulenko, Serge Erratum:
"Neural networks and reaction-diffusion systems with prescribed dynamics".
C. R. Acad. Sci. Paris S\'er. I Math. 325 (1997), no. 3, 287.
[47] Vakulenko, S. A. The boundary layer method for nonlinear
parabolic equations. (Russian) Differential equations. Spectral theory.
Wave propagation (Russian), 79--86, 306, Probl.
Mat. Fiz., 13, Leningrad. Univ., Leningrad, 1991.
[48] Vakulenko, S. A.; Molotkov, I. A. Whitham's and Fermat's
principles for the problem of evolution of wave beams in a
nonlinear inhomogeneous medium,
Wave
propagation. Scattering theory, 17--26, Amer. Math. Soc. Transl. Ser. 2,
157, Amer. Math. Soc., Providence, RI, 1993.
[49] Vakulenko, S. A.; Molotkov, I. A.
The Whitham principle and the Fermat principle in a problem on the evolution
of wave beams in a nonlinear inhomogeneous medium. (Russian)
Wave propagation. Scattering theory (Russian), 22--32, 256,
Probl. Mat. Fiz., 12, Leningrad. Univ., Leningrad, 1987.
[51] Babich, V. M.; Molotkov, I. A.; Vakulenko, S. A.
Asymptotic approach to some nonlinear wave problems.
Nonlinear deformation waves (Tallinn, 1982), 76--86, Springer,
Berlin-New York, 1983.
[52] Vakulenko, S. A.; Molotkov, I. A.
Waves in a nonlinear inhomogeneous medium that are concentrated in
the vicinity of a given curve. (Russian) Dokl. Akad. Nauk SSSR 262
(1982), no. 3, 587--591.
[53] Vakulenko, S. A. The boundary layer method for nonlinear
parabolic equations. (Russian) Differential equations. Spectral theory.
Wave propagation (Russian), 79--86, 306, Probl.
Mat. Fiz., 13, Leningrad. Univ., Leningrad, 1991.
[54] Vakoulenko, Serge, Complexit\'e dynamique
de reseaux de Hopfield, C. R. Acad. Sci. Paris S\'er.
I Math., T.335,
(2002).
[55] S. Vakulenko and D. Grigoriev,
Complexity of patterns generated by genetic
circuits and Pfaffian functions,
Preprint IHES, 2003.
[56]
S. Vakulenko and S. Genieys, Pattern programming
by genetic networks, Patterns and Waves,
S. Petersbourg 2003.
[57] V. M. Buren, S. A. Vakulenko,
Model of local cell differentiation in plants,Patterns and Waves,
S. Petersbourg 2003.
[58] Vakulenko S, Grigoriev D.
Complexity of gene circuits, Pfaffian functions and
morphogenesis problem, C. R. Acad. Sci. Paris,
S\'er. I Math., 2003.CRAS2.PS
[59] Vakulenko S, Grigoriev D.,
Stable growth of complex systems, Proceeding of Fifth Workshop
on Simulation, (2005) 705- 709.
[60]
S. Vakulenko. B. Kazmierchak, Attractor and Pattern Control
in Nonlinear Media by Localized Defects, 21-th Intern.
Congress of Theor. and Applied Mechanics, Warsaw, 2004,
Book of Extended abstacts p.218, Extended summary on CD-Rom.
[61] E. L. Aero, A. L. Fradkov, S. A. Vakulenko, B. R. Andrievsky,
Dynamic Problems of Nonlinear Oscillations and
Control of complex Crystalline Lattice, Proceedings of the
Third European Conference on Structural Control, V2, Vienna,
Austria, July, 2004.
[62] D. Grigoriev, A. Kazakov, S. Vakulenko, Quantum optical device,
accelerating dynamical programming, preprint.