Selected publications by Iliya D. Iliev

Monograph

(with E.Kh. Khristov and K.P. Kirchev) Spectral methods in soliton equations: Pitman Monographs and Surveys in Pure and Applied Mathematics 73,
Longman Scientific & Technical, Harlow (Co-published in the US with John Wiley & Sons) (1994),
pp x + 384, ISBN 0-582-23963-X, 0-470-23477-6.

Papers

(with S. Hakkaev and K. Kirchev) Stability of periodic traveling waves for complex modified Korteweg-de Vries equation: J. Differential Equations 248 (2010), no. 10, 2608-2627.
(with Chengzhi Li and Jiang Yu) Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes: Commun. Pure Appl. Anal. 9 (2010), no. 3, 583-610.
(with L. Gavrilov) Quadratic perturbations of quadratic codimension-four centers: J. Math. Anal. Appl. 357 (2009), no. 1, 69-76.
(with S. Gautier and L. Gavrilov) Perturbations of quadratic centers of genus one: Discrete Contin. Dynam. Systems A 25 (2009), no. 2, 511-535.
(with S. Hakkaev and K. Kirchev) Stability of periodic travelling shallow-water waves determined by Newton's equation [an article chosen for IOP Select]: J. Phys. A: Math. Theor. 41 (2008), no. 8.
(with L. Gavrilov) The displacement map associated to polynomial unfoldings of planar Hamiltonian vector fields: Amer. J. Math. 127 (2005), no. 6, 1153-1190.
(with Chengzhi Li and Jiang Yu) Bifurcations of limit cycles from quadratic non-Hamiltonian systems with two centres and two unbounded heteroclinic loops: Nonlinearity 18 (2005), no. 1, 305-330.
(with L. Gavrilov) Complete hyperelliptic integrals of the first kind and their non-oscillation: Trans. Amer. Math. Soc. 356 (2004), no. 3, 1185-1207.
(with L. Gavrilov) Two-dimensional Fuchsian systems and the Chebyshev property: J. Differential Equations 191 (2003), no. 1, 105-120.
(with L. Gavrilov) Bifurcations of limit cycles from infinity in quadratic systems: Canad. J. Math. 54 (2002), no. 5, 1038-1064.
Benjamin-Bona-Mahony equation: in: M. Hazewinkel (Managing Editor), Encyclopaedia of Mathematics, Suppl. III, pp. 66-67; Kluwer Academic Publishers, Dordrecht, The Netherlands (2002).
(with L. Gavrilov) Second order analysis in polynomially perturbed reversible quadratic Hamiltonian systems: Ergodic Theory Dynam. Systems 20 (2000), no. 6, 1671-1686.
On the limit cycles available from polynomial perturbations of the Bogdanov-Takens Hamiltonian: Israel J. Math. 115 (2000), 269-284.
The number of limit cycles due to polynomial perturbations of the harmonic oscillator: Math. Proc. Cambridge Philos. Soc. 127 (1999), no. 2, 317-322.
(with L.M. Perko) Higher order bifurcations of limit cycles: J. Differential Equations 154 (1999), no. 2, 339-363.
(with E. Horozov) Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians: Nonlinearity 11 (1998), no. 6, 1521-1537.
On second order bifurcations of limit cycles: J. London Math. Soc. (2) 58 (1998), no. 2, 353-366.
Perturbations of quadratic centers: Bull. Sci. Math. 122 (1998), no. 2, 107-161.
Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems: Proc. Roy. Soc. Edinburgh A 127 (1997), no. 6, 1207-1217.
The cyclicity of the period annulus of the quadratic Hamiltonian triangle: J. Differential Equations 128 (1996), no. 1, 309-326.
Higher order Melnikov functions for degenerate cubic Hamiltonians: Adv. Differential Equations 1 (1996), no. 4, 689-708.
(with E. Horozov) Perturbations of quadratic Hamiltonian systems with symmetry: Ann. Inst. H. Poincare, Anal. non lineaire 13 (1996), no. 1, 17-56.
(with E. Horozov) Hilbert-Arnold problem for cubic Hamiltonians and limit cycles: in: Proceedings of the Fourth International Colloquium on Differential Equations, pp. 115-124; VSP Intern. Sci. Publishers, Zeist, The Netherlands (1994).
(with E. Horozov) On the number of limit cycles in perturbations of quadratic Hamiltonian systems: Proc. Lond. Math. Soc. (3) 69 (1994), no. 1, 198-224.
(with E. Horozov) On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems: J. Differential Equations 113 (1994), no. 1, 84-105.
(with K.P. Kirchev) Stability and instability of solitary waves for one-dimensional singular Schroedinger equations: Differential Integral Equations 6 (1993), no. 3, 685-703.
(with K.P. Kirchev) The stability of traveling waves for nonlinear equations of the Benjamin-Bona-Mahony equation type: Math. Nachr. 141 (1989), 313-324. [Russian]
(with V. Petrov) Mathematical analysis of an aortic flow rate model with concentrated parameters: Theor. and Appl. Mech. 20 (1989), no. 3, 72-81.
(with K.P. Kirchev) Stability of soliton-like solutions for some nonlinear equations of mathematical physics: Mathematics and mathematical education, pp. 23-31, Bulgarian Acad. Sci. (1989). [Russian]
(with K.P. Kirchev) Stability of traveling waves for nonlinear equations of Korteweg-de Vries equations type: C. R. Acad. Bulgare Sci. 40 (1987), no. 7, 25-27. [Russian]
(with K.P. Kirchev) Stability of solutions of kink type for some nonlinear equations similar to the Korteweg-de Vries equation: Serdica 13 (1987), no. 4, 414-419. [Russian]
(with K.P. Kirchev) On the stability of traveling waves for nonlinear equations of Korteweg-de Vries type: Commun. JINR, P5-86-801 (1986), 11 pp. [Russian]
(with K.P. Kirchev) Stability of Hirota's single-soliton solution for an equation that generalizes the complex modified Korteweg-de Vries equation and a nonlinear Schroedinger equation: Commun. JINR, P5-86-46 (1986), 12 pp. [Russian]
(with E.P. Zhidkov and K.P. Kirchev) Stability of the solitary-wave solution to the nonlinear modified complex Korteweg-de Vries equation: Siberian Math. J. 26 (1985), no. 6, 39-47. [Russian]
(with E.P. Zhidkov and K.P. Kirchev) Stability of a solitary-wave solution to the Schroedinger equation with a power-type nonlinearity: Commun. JINR, P5-83-771 (1983), 12 pp. [Russian]
Initial boundary value problems for a class of higher order evolution equations: C. R. Acad. Bulgare Sci. 35 (1982), no. 5, 585-587.
An initial boundary value problem in a quarter space for a class of I.G. Petrovskii well-posed equations with variable coefficients: C. R. Acad. Bulgare Sci. 34 (1981), no. 7, 937-940. [Russian]
On the boundary problems in a half-space for a class of nonhypoelliptic equations with constant strength: Serdica 6 (1980), no. 3, 245-257.
On the boundary problems in a half-space for a class of nonhypoelliptic operators: C. R. Acad. Bulgare Sci. 33 (1980), no. 1, 43-46.
Smooth solutions of some nonhypoelliptic equations: Annuaire Univ. Sofia Fac. Math. Mech. 73 (1979), 93-96. [Bulgarian]
Smoothness of solutions in Rn of a class of nonhypoelliptic equations with constant strength: C. R. Acad. Bulgare Sci. 32 (1979), no. 4, 411-414.
Hypoellipticity for equations of constant strength: Mathematics and mathematical education, pp. 276-288, Bulgarian Acad. Sci. (1979). [Bulgarian]
Mixed problem for a class of parabolic equations with a multidimensional time variable: C. R. Acad. Bulgare Sci. 30 (1977), no. 11, 1525-1527.

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