Gavrilov, Lubomir; Iliev, Iliya D. The limit cycles in a generalized Rayleigh-Liénard oscillator. (English) Zbl 07689317 Discrete Contin. Dyn. Syst. 43, No. 6, 2381-2400 (2023). MSC: 34C05 34C07 34C08 PDF BibTeX XML Cite \textit{L. Gavrilov} and \textit{I. D. Iliev}, Discrete Contin. Dyn. Syst. 43, No. 6, 2381--2400 (2023; Zbl 07689317) Full Text: DOI arXiv
Gerdjikov, V. S.; Stefanov, A. A.; Iliev, I. D.; Boyadjiev, G. P.; Smirnov, A. O.; Matveev, V. B.; Pavlov, M. V. Recursion operators and hierarchies of mKdV equations related to the Kac-Moody algebras \(D_4^{(1)}\), \(D_4^{(2)}\), and \(D_4^{(3)}\). (English. Russian original) Zbl 1456.37072 Theor. Math. Phys. 204, No. 3, 1110-1129 (2020); translation from Teor. Mat. Fiz. 204, No. 3, 332-354 (2020). MSC: 37K10 37K20 35Q53 17B67 PDF BibTeX XML Cite \textit{V. S. Gerdjikov} et al., Theor. Math. Phys. 204, No. 3, 1110--1129 (2020; Zbl 1456.37072); translation from Teor. Mat. Fiz. 204, No. 3, 332--354 (2020) Full Text: DOI arXiv
Iliev, Iliya D.; Li, Chengzhi; Yu, Jiang On the cubic perturbations of the symmetric 8-loop Hamiltonian. (English) Zbl 1443.34040 J. Differ. Equations 269, No. 4, 3387-3413 (2020). MSC: 34C23 34C05 34E10 34C07 34C08 37J40 PDF BibTeX XML Cite \textit{I. D. Iliev} et al., J. Differ. Equations 269, No. 4, 3387--3413 (2020; Zbl 1443.34040) Full Text: DOI arXiv
Gavrilov, Lubomir; Iliev, Iliya D. Cubic perturbations of elliptic Hamiltonian vector fields of degree three. (English) Zbl 1342.34050 J. Differ. Equations 260, No. 5, 3963-3990 (2016). Reviewer: Valery A. Gaiko (Minsk) MSC: 34C07 34C23 34C05 34E10 PDF BibTeX XML Cite \textit{L. Gavrilov} and \textit{I. D. Iliev}, J. Differ. Equations 260, No. 5, 3963--3990 (2016; Zbl 1342.34050) Full Text: DOI arXiv
Gavrilov, Lubomir; Iliev, Iliya D. Perturbations of quadratic Hamiltonian two-saddle cycles. (English) Zbl 1374.34131 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 2, 307-324 (2015). MSC: 34C23 34C37 34C05 34C07 PDF BibTeX XML Cite \textit{L. Gavrilov} and \textit{I. D. Iliev}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 2, 307--324 (2015; Zbl 1374.34131) Full Text: DOI arXiv
Hakkaev, Sevdzhan; Iliev, Iliya D.; Kirchev, Kiril Stability of periodic traveling waves for the quadratic and cubic nonlinear schrödinger equations. (English) Zbl 1270.35081 Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 5, Article ID 1350090, 20 p. (2013). MSC: 35B35 35Q55 35C07 PDF BibTeX XML Cite \textit{S. Hakkaev} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 5, Article ID 1350090, 20 p. (2013; Zbl 1270.35081) Full Text: DOI arXiv
Christov, Ognyan; Hakkaev, Sevdzhan; Iliev, Iliya D. Non-uniform continuity of periodic Holm-Staley \(b\)-family of equations. (English) Zbl 1251.35123 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 13, 4821-4838 (2012). MSC: 35Q53 35C07 35B10 PDF BibTeX XML Cite \textit{O. Christov} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 13, 4821--4838 (2012; Zbl 1251.35123) Full Text: DOI arXiv
Iliev, Iliya D.; Li, Chengzhi; Yu, Jiang Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes. (English) Zbl 1198.34049 Commun. Pure Appl. Anal. 9, No. 3, 583-610 (2010). Reviewer: M. A. M. Alwash (Culver City) MSC: 34C07 34C08 37G15 34C23 34C14 PDF BibTeX XML Cite \textit{I. D. Iliev} et al., Commun. Pure Appl. Anal. 9, No. 3, 583--610 (2010; Zbl 1198.34049) Full Text: DOI
Hakkaev, Sevdzhan; Iliev, Iliya D.; Kirchev, Kiril Stability of periodic traveling waves for complex modified Korteweg-de Vries equation. (English) Zbl 1187.35211 J. Differ. Equations 248, No. 10, 2608-2627 (2010). MSC: 35Q53 35C07 35B10 35B35 35B60 PDF BibTeX XML Cite \textit{S. Hakkaev} et al., J. Differ. Equations 248, No. 10, 2608--2627 (2010; Zbl 1187.35211) Full Text: DOI arXiv
Gautier, Sébastien; Gavrilov, Lubomir; Iliev, Iliya D. Perturbations of quadratic centers of genus one. (English) Zbl 1178.34037 Discrete Contin. Dyn. Syst. 25, No. 2, 511-535 (2009). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34C07 34C08 37G15 PDF BibTeX XML Cite \textit{S. Gautier} et al., Discrete Contin. Dyn. Syst. 25, No. 2, 511--535 (2009; Zbl 1178.34037) Full Text: DOI arXiv
Gavrilov, Lubomir; Iliev, Iliya D. Quadratic perturbations of quadratic codimension-four centers. (English) Zbl 1177.34046 J. Math. Anal. Appl. 357, No. 1, 69-76 (2009). Reviewer: Alexey Remizov (Trieste) MSC: 34C07 34C05 34C08 34C23 PDF BibTeX XML Cite \textit{L. Gavrilov} and \textit{I. D. Iliev}, J. Math. Anal. Appl. 357, No. 1, 69--76 (2009; Zbl 1177.34046) Full Text: DOI arXiv
Hakkaev, Sevdzhan; Iliev, Iliya D.; Kirchev, Kiril Stability of periodic travelling shallow-water waves determined by Newton’s equation. (English) Zbl 1136.35317 J. Phys. A, Math. Theor. 41, No. 8, Article ID 085203, 31 p. (2008). MSC: 35B35 35B10 35Q35 35Q53 35B25 34C08 34L40 PDF BibTeX XML Cite \textit{S. Hakkaev} et al., J. Phys. A, Math. Theor. 41, No. 8, Article ID 085203, 31 p. (2008; Zbl 1136.35317) Full Text: DOI arXiv
Gavrilov, Lubomir; Iliev, Iliya D. The displacement map associated to polynomial unfoldings of planar Hamiltonian vector fields. (English) Zbl 1093.34015 Am. J. Math. 127, No. 6, 1153-1190 (2005). Reviewer: Valery A. Gaiko (Minsk) MSC: 34C07 37C10 37C27 58K05 58K10 34C08 PDF BibTeX XML Cite \textit{L. Gavrilov} and \textit{I. D. Iliev}, Am. J. Math. 127, No. 6, 1153--1190 (2005; Zbl 1093.34015) Full Text: DOI arXiv Link
Iliev, Iliya D.; Li, Chengzhi; Yu, Jiang Bifurcations of limit cycles from quadratic non-Hamiltonian systems with two centres and two unbounded heteroclinic loops. (English) Zbl 1077.34035 Nonlinearity 18, No. 1, 305-330 (2005). Reviewer: Valery A. Gaiko (Minsk) MSC: 34C07 37G15 34C08 34C23 PDF BibTeX XML Cite \textit{I. D. Iliev} et al., Nonlinearity 18, No. 1, 305--330 (2005; Zbl 1077.34035) Full Text: DOI
Gavrilov, Lubomir; Iliev, Iliya D. Complete hyperelliptic integrals of the first kind and their non-oscillation. (English) Zbl 1043.34031 Trans. Am. Math. Soc. 356, No. 3, 1185-1207 (2004). Reviewer: Jinghuang Tian (Phoenix) MSC: 34C08 34C07 14K20 PDF BibTeX XML Cite \textit{L. Gavrilov} and \textit{I. D. Iliev}, Trans. Am. Math. Soc. 356, No. 3, 1185--1207 (2004; Zbl 1043.34031) Full Text: DOI arXiv
Gavrilov, Lubomir; Iliev, Iliya D. Two-dimensional Fuchsian systems and the Chebyshev property. (English) Zbl 1046.34056 J. Differ. Equations 191, No. 1, 105-120 (2003). MSC: 34C08 34C05 34C07 37C25 PDF BibTeX XML Cite \textit{L. Gavrilov} and \textit{I. D. Iliev}, J. Differ. Equations 191, No. 1, 105--120 (2003; Zbl 1046.34056) Full Text: DOI arXiv
Gavrilov, Lubomir; Iliev, Iliya D. Bifurcations of limit cycles from infinity in quadratic systems. (English) Zbl 1026.34037 Can. J. Math. 54, No. 5, 1038-1064 (2002). Reviewer: Dimitrii Rachinskii (Moskva) MSC: 34C07 34C10 34C05 37G15 PDF BibTeX XML Cite \textit{L. Gavrilov} and \textit{I. D. Iliev}, Can. J. Math. 54, No. 5, 1038--1064 (2002; Zbl 1026.34037) Full Text: DOI
Gavrilov, Lubomir; Iliev, Iliya D. Second-order analysis in polynomially perturbed reversible quadratic Hamiltonian systems. (English) Zbl 0992.37054 Ergodic Theory Dyn. Syst. 20, No. 6, 1671-1686 (2000). Reviewer: Messoud Efendiev (Berlin) MSC: 37J40 70H09 34C07 PDF BibTeX XML Cite \textit{L. Gavrilov} and \textit{I. D. Iliev}, Ergodic Theory Dyn. Syst. 20, No. 6, 1671--1686 (2000; Zbl 0992.37054) Full Text: DOI
Iliev, Iliya D. On the limit cycles available from polynomial perturbations of the Bogdanov-Takens Hamiltonian. (English) Zbl 0945.34020 Isr. J. Math. 115, 269-284 (2000). MSC: 34C07 34C05 37J05 37J40 PDF BibTeX XML Cite \textit{I. D. Iliev}, Isr. J. Math. 115, 269--284 (2000; Zbl 0945.34020) Full Text: DOI
Iliev, Iliya D. The number of limit cycles due to polynomial perturbations of the harmonic oscillator. (English) Zbl 0967.34026 Math. Proc. Camb. Philos. Soc. 127, No. 2, 317-322 (1999). Reviewer: Klaus R.Schneider (Berlin) MSC: 34C07 34C05 34C15 PDF BibTeX XML Cite \textit{I. D. Iliev}, Math. Proc. Camb. Philos. Soc. 127, No. 2, 317--322 (1999; Zbl 0967.34026) Full Text: DOI
Iliev, I. D.; Perko, L. M. Higher order bifurcations of limit cycles. (English) Zbl 0926.34033 J. Differ. Equations 154, No. 2, 339-363 (1999). MSC: 34C23 34C05 37G15 37J20 PDF BibTeX XML Cite \textit{I. D. Iliev} and \textit{L. M. Perko}, J. Differ. Equations 154, No. 2, 339--363 (1999; Zbl 0926.34033) Full Text: DOI
Iliev, I. D. On second order bifurcations of limit cycles. (English) Zbl 0922.34037 J. Lond. Math. Soc., II. Ser. 58, No. 2, 353-366 (1998). Reviewer: I.D.Iliev (Sofia) MSC: 34C23 37G15 37G99 37J40 34C05 PDF BibTeX XML Cite \textit{I. D. Iliev}, J. Lond. Math. Soc., II. Ser. 58, No. 2, 353--366 (1998; Zbl 0922.34037) Full Text: DOI
Horozov, Emil; Iliev, Iliya D. Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians. (English) Zbl 0921.58044 Nonlinearity 11, No. 6, 1521-1537 (1998). Reviewer: E.Ershov (St.Peterburg) MSC: 37G15 37J20 37K50 34C05 PDF BibTeX XML Cite \textit{E. Horozov} and \textit{I. D. Iliev}, Nonlinearity 11, No. 6, 1521--1537 (1998; Zbl 0921.58044) Full Text: DOI
Iliev, Iliya D. Perturbations of quadratic centers. (English) Zbl 0920.34037 Bull. Sci. Math. 122, No. 2, 107-161 (1998). Reviewer: C.Chicone (Columbia) MSC: 34C05 37G15 PDF BibTeX XML Cite \textit{I. D. Iliev}, Bull. Sci. Math. 122, No. 2, 107--161 (1998; Zbl 0920.34037) Full Text: DOI
Iliev, Iliya D. Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems. (English) Zbl 0896.34019 Proc. R. Soc. Edinb., Sect. A, Math. 127, No. 6, 1207-1217 (1997). Reviewer: J.Knobloch (Ilmenau) MSC: 34C05 37G15 34C23 PDF BibTeX XML Cite \textit{I. D. Iliev}, Proc. R. Soc. Edinb., Sect. A, Math. 127, No. 6, 1207--1217 (1997; Zbl 0896.34019) Full Text: DOI
Iliev, Iliya D. The cyclicity of the period annulus of the quadratic Hamiltonian triangle. (English) Zbl 0853.58084 J. Differ. Equations 128, No. 1, 309-326 (1996). Reviewer: G.Osipenko (St.Peterburg) MSC: 37G15 34C05 37E99 37G99 PDF BibTeX XML Cite \textit{I. D. Iliev}, J. Differ. Equations 128, No. 1, 309--326 (1996; Zbl 0853.58084) Full Text: DOI
Iliev, I. D. Higher-order Melnikov functions for degenerate cubic Hamiltonians. (English) Zbl 0851.34042 Adv. Differ. Equ. 1, No. 4, 689-708 (1996). Reviewer: Ye Yanqian (Nanjing) MSC: 34C23 34C05 37G15 PDF BibTeX XML Cite \textit{I. D. Iliev}, Adv. Differ. Equ. 1, No. 4, 689--708 (1996; Zbl 0851.34042)
Horozov, Emil Ivanov; Iliev, Iliya Dimov Perturbations of quadratic Hamiltonian systems with symmetry. (English) Zbl 0854.34035 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 13, No. 1, 17-56 (1996). Reviewer: Yu.V.Rogovchenko (Kiev) MSC: 34C05 37J99 34C23 34D10 PDF BibTeX XML Cite \textit{E. I. Horozov} and \textit{I. D. Iliev}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 13, No. 1, 17--56 (1996; Zbl 0854.34035) Full Text: DOI Numdam EuDML
Horozov, E.; Iliev, I. D. Hilbert-Arnold problem for cubic Hamiltonians and limit cycles. (English) Zbl 0843.34037 Bainov, D. (ed.) et al., Proceedings of the fourth international colloquium on differential equations, Plovdiv, Bulgaria, August 18-22, 1993. Utrecht: VSP. 115-124 (1994). MSC: 34C05 PDF BibTeX XML Cite \textit{E. Horozov} and \textit{I. D. Iliev}, in: Proceedings of the fourth international colloquium on differential equations, Plovdiv, Bulgaria, August 18-22, 1993. Utrecht: VSP. 115--124 (1994; Zbl 0843.34037)
Iliev, I. D.; Khristov, E. Kh.; Kirchev, K. P. Spectral methods in soliton equations. (English) Zbl 0874.35104 Pitman Monographs and Surveys in Pure and Applied Mathematics. 73. Harlow: Longman Scientific & Technical. New York, NY: John Wiley & Sons, Inc. x, 384 p. (1994). Reviewer: T.Aktosun (Fargo) MSC: 35Q51 35Q53 35B35 35R30 35-02 PDF BibTeX XML Cite \textit{I. D. Iliev} et al., Spectral methods in soliton equations. Harlow: Longman Scientific \& Technical; New York, NY: John Wiley \& Sons, Inc. (1994; Zbl 0874.35104)
Horozov, E.; Iliev, I. D. On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems. (English) Zbl 0808.34041 J. Differ. Equations 113, No. 1, 84-105 (1994). Reviewer: M.A.Teixeira (Campinas) MSC: 34C23 34C05 37J99 37G15 PDF BibTeX XML Cite \textit{E. Horozov} and \textit{I. D. Iliev}, J. Differ. Equations 113, No. 1, 84--105 (1994; Zbl 0808.34041) Full Text: DOI
Horozov, E.; Iliev, I. D. On the number of limit cycles in perturbations of quadratic Hamiltonian systems. (English) Zbl 0802.58046 Proc. Lond. Math. Soc., III. Ser. 69, No. 1, 198-224 (1994). Reviewer: E.Horozov (Sofia) MSC: 37G15 34C05 PDF BibTeX XML Cite \textit{E. Horozov} and \textit{I. D. Iliev}, Proc. Lond. Math. Soc. (3) 69, No. 1, 198--224 (1994; Zbl 0802.58046) Full Text: DOI
Iliev, Ilya D.; Kirchev, Kiril P. Stability and instability of solitary waves for one-dimensional singular Schrödinger equations. (English) Zbl 0783.35071 Differ. Integral Equ. 6, No. 3, 685-703 (1993). Reviewer: B.A.Malomed (Ramat Aviv) MSC: 35Q55 35B35 35Q51 PDF BibTeX XML Cite \textit{I. D. Iliev} and \textit{K. P. Kirchev}, Differ. Integral Equ. 6, No. 3, 685--703 (1993; Zbl 0783.35071)
Iliev, I.; Petrov, V. Mathematical analysis of an aortic flow rate model with concentrated parameters. (English) Zbl 0698.76130 Teor. Prilozhna Mekh. 1989, No. 3, 72-81 (1989). MSC: 76Z05 PDF BibTeX XML Cite \textit{I. Iliev} and \textit{V. Petrov}, Teor. Prilozhna Mekh. 1989, No. 3, 72--81 (1989; Zbl 0698.76130)
Iliev, I. D.; Kirchev, K. P. On the stability of running waves for non-linear equations of Benjamin- Bona-Mahony type. (Russian) Zbl 0688.35087 Math. Nachr. 141, 313-324 (1989). Reviewer: I.D.Iliev MSC: 35Q99 35B35 35K55 PDF BibTeX XML Cite \textit{I. D. Iliev} and \textit{K. P. Kirchev}, Math. Nachr. 141, 313--324 (1989; Zbl 0688.35087) Full Text: DOI
Iliev, I. D.; Kirchev, K. P. Stability of the kink form solutions for some nonlinear equations similar to the Korteweg-de Vries equation. (Russian) Zbl 0696.35137 Serdica 13, 414-419 (1987). Reviewer: J.H.Tian MSC: 35Q99 PDF BibTeX XML Cite \textit{I. D. Iliev} and \textit{K. P. Kirchev}, Serdica 13, 414--419 (1987; Zbl 0696.35137)
Iliev, I. D.; Kirchev, K. P. Stability of travelling waves for nonlinear equations of Korteweg-de Vries type. (Russian) Zbl 0636.35074 C. R. Acad. Bulg. Sci. 40, No. 7, 25-27 (1987). Reviewer: I.D.Iliev MSC: 35Q99 35B40 35B05 PDF BibTeX XML Cite \textit{I. D. Iliev} and \textit{K. P. Kirchev}, C. R. Acad. Bulg. Sci. 40, No. 7, 25--27 (1987; Zbl 0636.35074)
Iliev, Iliya D. Smooth solutions of some nonhypoelliptic equations. (Bulgarian. English summary) Zbl 0636.35013 God. Sofij. Univ., Fak. Mat. Mekh. 73(1979), 93-96 (1986). MSC: 35B65 35G05 PDF BibTeX XML Cite \textit{I. D. Iliev}, God. Sofiĭ. Univ., Fak. Mat. Mekh. 73, 93--96 (1986; Zbl 0636.35013)
Zhidkov, E. P.; Iliev, I. D.; Kirchev, K. P. Stability of a solution of the form of a solitary wave for a nonlinear complex modified Korteweg-de Vries equation. (English. Russian original) Zbl 0597.35103 Sib. Math. J. 26, 810-817 (1985); translation from Sib. Mat. Zh. 26, No. 6(154), 39-47 (1985). Reviewer: E.D.Belokolos MSC: 35Q99 35B35 35A05 PDF BibTeX XML Cite \textit{E. P. Zhidkov} et al., Sib. Math. J. 26, 810--817 (1985; Zbl 0597.35103); translation from Sib. Mat. Zh. 26, No. 6(154), 39--47 (1985) Full Text: DOI
Iliev, I. D. Initial boundary value problems for a class of higher order evolution equations. (English) Zbl 0509.35019 C. R. Acad. Bulg. Sci. 35, 585-587 (1982). MSC: 35G15 35G10 35A05 35K25 35L25 PDF BibTeX XML Cite \textit{I. D. Iliev}, C. R. Acad. Bulg. Sci. 35, 585--587 (1982; Zbl 0509.35019)
Iliev, I. D. A mixed boundary value problem in a quarter-space for a certain class of in the sense of I. G. Petrovskij correct equations with variable coefficients. (Russian) Zbl 0485.35026 C. R. Acad. Bulg. Sci. 34, 937-940 (1981). MSC: 35G15 35A22 35B45 PDF BibTeX XML Cite \textit{I. D. Iliev}, C. R. Acad. Bulg. Sci. 34, 937--940 (1981; Zbl 0485.35026)
Iliev, I. D. On the boundary problems in a half-space for a class of nonhypoelliptic operators. (English) Zbl 0436.35019 C. R. Acad. Bulg. Sci. 33, 43-46 (1980). MSC: 35B65 65H10 PDF BibTeX XML Cite \textit{I. D. Iliev}, C. R. Acad. Bulg. Sci. 33, 43--46 (1980; Zbl 0436.35019)
Iliev, Iliya Hypoellipticity of equations with constant force. (Bulgarian) Zbl 0456.35017 Mathematics and education in mathematics, Proc. 8th Spring Conf. Union Bulg. Math., Sunny Beach 1979, 276-288 (1979). MSC: 35H10 PDF BibTeX XML
Iliev, I. D. Smoothness of solutions in \(R^n\) of a class of nonhypoelliptic equations with constant strength. (English) Zbl 0436.35018 C. R. Acad. Bulg. Sci. 32, 411-414 (1979). MSC: 35B65 35B45 65H10 PDF BibTeX XML Cite \textit{I. D. Iliev}, C. R. Acad. Bulg. Sci. 32, 411--414 (1979; Zbl 0436.35018)