## Iliev, Iliya Dimov

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 Author ID: iliev.iliya-dimov Published as: Iliev, Iliya D.; Iliev, I. D.; Iliev, Iliya Dimov; Iliev, Ilya D.; Iliev, Iliya; Iliev, I.
 Documents Indexed: 45 Publications since 1979, including 1 Book Reviewing Activity: 142 Reviews Co-Authors: 17 Co-Authors with 29 Joint Publications 335 Co-Co-Authors
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### Co-Authors

 14 single-authored 9 Gavrilov, Lubomir 9 Kirchev, Kiril P. 5 Khorozov, Emil Ivanov 4 Hakkaev, Sevdzhan A. 3 Li, Chengzhi 3 Yu, Jiang 1 Boyadjiev, G. P. 1 Christov, Ognyan 1 Ganev, D. 1 Gautier, Sébastien 1 Gerdzhikov, Vladimir Stefanov 1 Khristov, Evgeni Khristov 1 Matveev, Vladimir B. 1 Pavlov, Maxim V. 1 Perko, Lawrence M. 1 Smirnov, Alexander O. 1 Stefanov, Aleksander A. 1 Zhidkov, Eugeni P.
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### Serials

 7 Journal of Differential Equations 5 Doklady Bolgarskoĭ Akademii Nauk 2 Nonlinearity 2 Teoretichna i Prilozhna Mekhanika 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Theoretical and Mathematical Physics 1 American Journal of Mathematics 1 Canadian Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Nachrichten 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the London Mathematical Society. Third Series 1 Siberian Mathematical Journal 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Nauchni Trudove 1 Differential and Integral Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Serdica 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Bulletin des Sciences Mathématiques 1 Advances in Differential Equations 1 Discrete and Continuous Dynamical Systems 1 Communications on Pure and Applied Analysis 1 Pitman Monographs and Surveys in Pure and Applied Mathematics 1 Journal of Physics A: Mathematical and Theoretical 1 Godishnik na Sofiskiya Universitet. Fakultet po Matematika i Mekhanika
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### Fields

 26 Ordinary differential equations (34-XX) 20 Dynamical systems and ergodic theory (37-XX) 17 Partial differential equations (35-XX) 3 Mechanics of particles and systems (70-XX) 2 Numerical analysis (65-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX)

### Citations contained in zbMATH Open

34 Publications have been cited 642 times in 326 Documents Cited by Year
Perturbations of quadratic centers. Zbl 0920.34037
Iliev, Iliya D.
1998
On the number of limit cycles in perturbations of quadratic Hamiltonian systems. Zbl 0802.58046
Horozov, E.; Iliev, I. D.
1994
Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians. Zbl 0921.58044
Horozov, Emil; Iliev, Iliya D.
1998
Higher-order Melnikov functions for degenerate cubic Hamiltonians. Zbl 0851.34042
Iliev, I. D.
1996
The cyclicity of the period annulus of the quadratic Hamiltonian triangle. Zbl 0853.58084
Iliev, Iliya D.
1996
Perturbations of quadratic centers of genus one. Zbl 1178.34037
Gautier, Sébastien; Gavrilov, Lubomir; Iliev, Iliya D.
2009
The number of limit cycles due to polynomial perturbations of the harmonic oscillator. Zbl 0967.34026
Iliev, Iliya D.
1999
Higher order bifurcations of limit cycles. Zbl 0926.34033
Iliev, I. D.; Perko, L. M.
1999
Quadratic perturbations of quadratic codimension-four centers. Zbl 1177.34046
Gavrilov, Lubomir; Iliev, Iliya D.
2009
The displacement map associated to polynomial unfoldings of planar Hamiltonian vector fields. Zbl 1093.34015
Gavrilov, Lubomir; Iliev, Iliya D.
2005
On second order bifurcations of limit cycles. Zbl 0922.34037
Iliev, I. D.
1998
Bifurcations of limit cycles from quadratic non-Hamiltonian systems with two centres and two unbounded heteroclinic loops. Zbl 1077.34035
Iliev, Iliya D.; Li, Chengzhi; Yu, Jiang
2005
Complete hyperelliptic integrals of the first kind and their non-oscillation. Zbl 1043.34031
Gavrilov, Lubomir; Iliev, Iliya D.
2004
Stability of periodic travelling shallow-water waves determined by Newton’s equation. Zbl 1136.35317
Hakkaev, Sevdzhan; Iliev, Iliya D.; Kirchev, Kiril
2008
On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems. Zbl 0808.34041
Horozov, E.; Iliev, I. D.
1994
Second-order analysis in polynomially perturbed reversible quadratic Hamiltonian systems. Zbl 0992.37054
Gavrilov, Lubomir; Iliev, Iliya D.
2000
On the limit cycles available from polynomial perturbations of the Bogdanov-Takens Hamiltonian. Zbl 0945.34020
Iliev, Iliya D.
2000
Spectral methods in soliton equations. Zbl 0874.35104
Iliev, I. D.; Khristov, E. Kh.; Kirchev, K. P.
1994
Two-dimensional Fuchsian systems and the Chebyshev property. Zbl 1046.34056
Gavrilov, Lubomir; Iliev, Iliya D.
2003
Stability and instability of solitary waves for one-dimensional singular Schrödinger equations. Zbl 0783.35071
Iliev, Ilya D.; Kirchev, Kiril P.
1993
Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes. Zbl 1198.34049
Iliev, Iliya D.; Li, Chengzhi; Yu, Jiang
2010
Stability of periodic traveling waves for complex modified Korteweg-de Vries equation. Zbl 1187.35211
Hakkaev, Sevdzhan; Iliev, Iliya D.; Kirchev, Kiril
2010
Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems. Zbl 0896.34019
Iliev, Iliya D.
1997
Cubic perturbations of elliptic Hamiltonian vector fields of degree three. Zbl 1342.34050
Gavrilov, Lubomir; Iliev, Iliya D.
2016
Perturbations of quadratic Hamiltonian two-saddle cycles. Zbl 1374.34131
Gavrilov, Lubomir; Iliev, Iliya D.
2015
Bifurcations of limit cycles from infinity in quadratic systems. Zbl 1026.34037
Gavrilov, Lubomir; Iliev, Iliya D.
2002
Stability of a solution of the form of a solitary wave for a nonlinear complex modified Korteweg-de Vries equation. Zbl 0597.35103
Zhidkov, E. P.; Iliev, I. D.; Kirchev, K. P.
1985
Perturbations of quadratic Hamiltonian systems with symmetry. Zbl 0854.34035
Horozov, Emil Ivanov; Iliev, Iliya Dimov
1996
Hilbert-Arnold problem for cubic Hamiltonians and limit cycles. Zbl 0843.34037
Horozov, E.; Iliev, I. D.
1994
Non-uniform continuity of periodic Holm-Staley $$b$$-family of equations. Zbl 1251.35123
Christov, Ognyan; Hakkaev, Sevdzhan; Iliev, Iliya D.
2012
Stability of periodic traveling waves for the quadratic and cubic nonlinear schrödinger equations. Zbl 1270.35081
Hakkaev, Sevdzhan; Iliev, Iliya D.; Kirchev, Kiril
2013
Recursion operators and hierarchies of mKdV equations related to the Kac-Moody algebras $$D_4^{(1)}$$, $$D_4^{(2)}$$, and $$D_4^{(3)}$$. Zbl 1456.37072
Gerdjikov, V. S.; Stefanov, A. A.; Iliev, I. D.; Boyadjiev, G. P.; Smirnov, A. O.; Matveev, V. B.; Pavlov, M. V.
2020
On the stability of running waves for non-linear equations of Benjamin- Bona-Mahony type. Zbl 0688.35087
Iliev, I. D.; Kirchev, K. P.
1989
On the cubic perturbations of the symmetric 8-loop Hamiltonian. Zbl 1443.34040
Iliev, Iliya D.; Li, Chengzhi; Yu, Jiang
2020
Recursion operators and hierarchies of mKdV equations related to the Kac-Moody algebras $$D_4^{(1)}$$, $$D_4^{(2)}$$, and $$D_4^{(3)}$$. Zbl 1456.37072
Gerdjikov, V. S.; Stefanov, A. A.; Iliev, I. D.; Boyadjiev, G. P.; Smirnov, A. O.; Matveev, V. B.; Pavlov, M. V.
2020
On the cubic perturbations of the symmetric 8-loop Hamiltonian. Zbl 1443.34040
Iliev, Iliya D.; Li, Chengzhi; Yu, Jiang
2020
Cubic perturbations of elliptic Hamiltonian vector fields of degree three. Zbl 1342.34050
Gavrilov, Lubomir; Iliev, Iliya D.
2016
Perturbations of quadratic Hamiltonian two-saddle cycles. Zbl 1374.34131
Gavrilov, Lubomir; Iliev, Iliya D.
2015
Stability of periodic traveling waves for the quadratic and cubic nonlinear schrödinger equations. Zbl 1270.35081
Hakkaev, Sevdzhan; Iliev, Iliya D.; Kirchev, Kiril
2013
Non-uniform continuity of periodic Holm-Staley $$b$$-family of equations. Zbl 1251.35123
Christov, Ognyan; Hakkaev, Sevdzhan; Iliev, Iliya D.
2012
Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes. Zbl 1198.34049
Iliev, Iliya D.; Li, Chengzhi; Yu, Jiang
2010
Stability of periodic traveling waves for complex modified Korteweg-de Vries equation. Zbl 1187.35211
Hakkaev, Sevdzhan; Iliev, Iliya D.; Kirchev, Kiril
2010
Perturbations of quadratic centers of genus one. Zbl 1178.34037
Gautier, Sébastien; Gavrilov, Lubomir; Iliev, Iliya D.
2009
Quadratic perturbations of quadratic codimension-four centers. Zbl 1177.34046
Gavrilov, Lubomir; Iliev, Iliya D.
2009
Stability of periodic travelling shallow-water waves determined by Newton’s equation. Zbl 1136.35317
Hakkaev, Sevdzhan; Iliev, Iliya D.; Kirchev, Kiril
2008
The displacement map associated to polynomial unfoldings of planar Hamiltonian vector fields. Zbl 1093.34015
Gavrilov, Lubomir; Iliev, Iliya D.
2005
Bifurcations of limit cycles from quadratic non-Hamiltonian systems with two centres and two unbounded heteroclinic loops. Zbl 1077.34035
Iliev, Iliya D.; Li, Chengzhi; Yu, Jiang
2005
Complete hyperelliptic integrals of the first kind and their non-oscillation. Zbl 1043.34031
Gavrilov, Lubomir; Iliev, Iliya D.
2004
Two-dimensional Fuchsian systems and the Chebyshev property. Zbl 1046.34056
Gavrilov, Lubomir; Iliev, Iliya D.
2003
Bifurcations of limit cycles from infinity in quadratic systems. Zbl 1026.34037
Gavrilov, Lubomir; Iliev, Iliya D.
2002
Second-order analysis in polynomially perturbed reversible quadratic Hamiltonian systems. Zbl 0992.37054
Gavrilov, Lubomir; Iliev, Iliya D.
2000
On the limit cycles available from polynomial perturbations of the Bogdanov-Takens Hamiltonian. Zbl 0945.34020
Iliev, Iliya D.
2000
The number of limit cycles due to polynomial perturbations of the harmonic oscillator. Zbl 0967.34026
Iliev, Iliya D.
1999
Higher order bifurcations of limit cycles. Zbl 0926.34033
Iliev, I. D.; Perko, L. M.
1999
Perturbations of quadratic centers. Zbl 0920.34037
Iliev, Iliya D.
1998
Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians. Zbl 0921.58044
Horozov, Emil; Iliev, Iliya D.
1998
On second order bifurcations of limit cycles. Zbl 0922.34037
Iliev, I. D.
1998
Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems. Zbl 0896.34019
Iliev, Iliya D.
1997
Higher-order Melnikov functions for degenerate cubic Hamiltonians. Zbl 0851.34042
Iliev, I. D.
1996
The cyclicity of the period annulus of the quadratic Hamiltonian triangle. Zbl 0853.58084
Iliev, Iliya D.
1996
Perturbations of quadratic Hamiltonian systems with symmetry. Zbl 0854.34035
Horozov, Emil Ivanov; Iliev, Iliya Dimov
1996
On the number of limit cycles in perturbations of quadratic Hamiltonian systems. Zbl 0802.58046
Horozov, E.; Iliev, I. D.
1994
On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems. Zbl 0808.34041
Horozov, E.; Iliev, I. D.
1994
Spectral methods in soliton equations. Zbl 0874.35104
Iliev, I. D.; Khristov, E. Kh.; Kirchev, K. P.
1994
Hilbert-Arnold problem for cubic Hamiltonians and limit cycles. Zbl 0843.34037
Horozov, E.; Iliev, I. D.
1994
Stability and instability of solitary waves for one-dimensional singular Schrödinger equations. Zbl 0783.35071
Iliev, Ilya D.; Kirchev, Kiril P.
1993
On the stability of running waves for non-linear equations of Benjamin- Bona-Mahony type. Zbl 0688.35087
Iliev, I. D.; Kirchev, K. P.
1989
Stability of a solution of the form of a solitary wave for a nonlinear complex modified Korteweg-de Vries equation. Zbl 0597.35103
Zhidkov, E. P.; Iliev, I. D.; Kirchev, K. P.
1985
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### Cited by 308 Authors

 30 Han, Maoan 27 Zhao, Yulin 22 Llibre, Jaume 17 Gavrilov, Lubomir 15 Iliev, Iliya Dimov 14 Li, Chengzhi 12 Liu, Changjian 11 Gasull, Armengol 11 Xiao, Dongmei 11 Yang, Jihua 10 Asheghi, Rasoul 10 Zhao, Liqin 9 Hakkaev, Sevdzhan A. 9 Peng, Linping 9 Torregrosa, Joan 8 Novikov, Dmitry 8 Yu, Pei 8 Zhang, Tonghua 7 Françoise, Jean-Pierre 7 Mardešić, Pavao 7 Zhang, Zhifen 6 Cen, Xiuli 6 Liang, Haihua 6 Rebollo-Perdomo, Salomón 6 Wang, Jihua 6 Xiong, Yanqin 6 Yu, Jiang 6 Zang, Hong 5 Li, Cuiping 5 Wu, Kuilin 5 Zangeneh, Hamid R. Z. 4 Ben Hamed, Bassem 4 Feng, Zhaosheng 4 Gargouri, Ameni 4 Gerdzhikov, Vladimir Stefanov 4 Li, Shimin 4 Li, Tao 4 Li, Weigu 4 Ohta, Masahito 4 Pastor, Ademir 4 Pontigo-Herrera, Jessie 4 Tian, Yun 4 Uribe, Marco 3 Bakhshalizadeh, Ali 3 Buică, Adriana 3 Buzzi, Claudio Aguinaldo 3 Giné, Jaume 3 Grau, Maite 3 Hong, Xiaochun 3 Huang, Bo 3 Johnson, Tomas 3 Mañosas, Francesc 3 Nabavi, Arefeh 3 Ortiz-Bobadilla, Laura 3 Prohens, Rafel 3 Shao, Yi 3 Sun, Xianbo 3 Tucker, Warwick 3 Yakovenko, Sergei 3 Yang, Junmin 3 Yang, Peixing 2 Arruda, Lynnyngs Kelly 2 Artés, Joan Carles 2 Banquet Brango, Carlos 2 Boyadjiev, Todor L. 2 Chen, Aiyong 2 Chen, Wencheng 2 Chen, Xingwu 2 de Andrade, Thiago Pinguello 2 Dumortier, Freddy 2 Freire, Igor Leite 2 Gaiko, Valery A. 2 Gao, Jing 2 Gao, Yunfei 2 Geng, Wei 2 Georgiev, Zhivko Dimitrov 2 Gramchev, Todor V. 2 Jebrane, Ahmed 2 Jiang, Jiao 2 Ke, Ai 2 Kirchev, Kiril P. 2 Li, Jibin 2 Li, Jinming 2 Liang, Feng 2 Ma, LiYuan 2 Medrado, João C. R. 2 Movasati, Hossein 2 Natali, Fábio M. Amorin 2 Qi, Minghui 2 Roussarie, Robert 2 Roytvarf, Nina 2 Saavedra, Mariana 2 Schlomiuk, Dana I. 2 Shang, Desheng 2 Shen, Shoufeng 2 Stefanov, Aleksander A. 2 Stefanov, Atanas G. 2 Sui, Shiyou 2 Tadé, Moses O. 2 Tian, Yuchu ...and 208 more Authors
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### Cited in 84 Serials

 56 Journal of Differential Equations 43 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 30 Journal of Mathematical Analysis and Applications 16 Bulletin des Sciences Mathématiques 15 Qualitative Theory of Dynamical Systems 12 Chaos, Solitons and Fractals 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Physica D 6 Journal of Dynamical and Control Systems 6 Nonlinear Analysis. Real World Applications 5 Applied Mathematics and Computation 4 Transactions of the American Mathematical Society 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Journal of Dynamics and Differential Equations 4 Communications on Pure and Applied Analysis 4 Mediterranean Journal of Mathematics 3 Israel Journal of Mathematics 3 Theoretical and Mathematical Physics 3 Chinese Annals of Mathematics. Series B 3 Applied Mathematics Letters 3 Science in China. Series A 3 Acta Mathematica Sinica. English Series 3 Dynamical Systems 3 Discrete and Continuous Dynamical Systems. Series B 3 Bulletin of the Brazilian Mathematical Society. New Series 2 Computers & Mathematics with Applications 2 Journal of Mathematical Physics 2 Rocky Mountain Journal of Mathematics 2 Reviews in Mathematical Physics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal of Difference Equations and Applications 2 Discrete and Continuous Dynamical Systems 2 Nonlinear Dynamics 2 Communications in Nonlinear Science and Numerical Simulation 2 Science China. Mathematics 2 Journal of Applied Analysis and Computation 2 Nonlinear Analysis. Theory, Methods & Applications 1 Communications in Mathematical Physics 1 Fluid Dynamics 1 Inverse Problems 1 Mathematical Methods in the Applied Sciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physics Letters. A 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Archiv der Mathematik 1 Duke Mathematical Journal 1 International Journal of Circuit Theory and Applications 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Kodai Mathematical Journal 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Proceedings of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Studies in Applied Mathematics 1 Ergodic Theory and Dynamical Systems 1 Applied Mathematics and Mechanics. (English Edition) 1 Mathematical and Computer Modelling 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal of Mathematical Sciences (New York) 1 Electronic Research Announcements of the American Mathematical Society 1 Differential Equations and Dynamical Systems 1 Chaos 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Discrete Dynamics in Nature and Society 1 Annals of Mathematics. Second Series 1 Regular and Chaotic Dynamics 1 Journal of Nonlinear Mathematical Physics 1 Differential Equations 1 Journal of the Australian Mathematical Society 1 Portugaliae Mathematica. Nova Série 1 Advanced Nonlinear Studies 1 Advances in Difference Equations 1 Communications in Mathematical Analysis 1 Frontiers of Mathematics in China 1 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Annales Henri Lebesgue 1 Mechanics of Solids
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### Cited in 23 Fields

 262 Ordinary differential equations (34-XX) 134 Dynamical systems and ergodic theory (37-XX) 46 Partial differential equations (35-XX) 18 Algebraic geometry (14-XX) 6 Several complex variables and analytic spaces (32-XX) 5 Functions of a complex variable (30-XX) 5 Numerical analysis (65-XX) 4 Mechanics of particles and systems (70-XX) 3 Nonassociative rings and algebras (17-XX) 3 Approximations and expansions (41-XX) 3 Fluid mechanics (76-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX)