Gerdjikov, Vladimir S. Nonlinear evolution equations related to Kac-Moody algebras \(A_r^{(1)}\): spectral aspects. (English) Zbl 1500.35258 Turk. J. Math. 46, No. 5, SI-2, 1828-1844 (2022). Reviewer: Ayman Kachmar (Nabaṭiyya) MSC: 35Q55 35Q15 35Q53 35B40 37K35 35K15 17B67 17B81 81R10 PDFBibTeX XMLCite \textit{V. S. Gerdjikov}, Turk. J. Math. 46, No. 5, 1828--1844 (2022; Zbl 1500.35258) Full Text: DOI
Gerdjikov, V. S.; Todorov, M. D.; Kyuldjiev, A. V. Adiabatic interactions of Manakov solitons – effects of cross-modulation. (English) Zbl 1461.35194 Wave Motion 71, 71-81 (2017). MSC: 35Q51 76Y05 81V19 82D10 PDFBibTeX XMLCite \textit{V. S. Gerdjikov} et al., Wave Motion 71, 71--81 (2017; Zbl 1461.35194) Full Text: DOI arXiv
Sekigawa, Kouei (ed.); Gerdjikov, Vladimir (ed.); Matsushita, Yasuo (ed.); Mladenov, Ivaïlo (ed.) International workshop on complex structures, integrability and vector fields, Sofia, Bulgaria, September 13–17, 2010. (English) Zbl 1217.00023 AIP Conference Proceedings 1340. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0895-1/pbk). viii, 245 p. (2011). MSC: 00B25 35-06 53-06 37-06 70-06 74-06 78-06 81-06 PDFBibTeX XMLCite \textit{K. Sekigawa} (ed.) et al., International workshop on complex structures, integrability and vector fields, Sofia, Bulgaria, September 13--17, 2010. Melville, NY: American Institute of Physics (AIP) (2011; Zbl 1217.00023)
Gerdjikov, Vladimir S. On spectral theory of Lax operators on symmetric spaces: vanishing versus constant boundary conditions. (English) Zbl 1205.35292 Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 10th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 6–11, 2008. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-323-531-5/pbk). 88-123 (2009). Reviewer: Q. P. Liu (Beijing) MSC: 35Q55 37K15 35Q15 78A46 35A08 81U40 PDFBibTeX XMLCite \textit{V. S. Gerdjikov}, in: Proceedings of the 10th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 6--11, 2008. Sofia: Avangard Prima. 88--123 (2009; Zbl 1205.35292)
Sekigawa, Kouei (ed.); Gerdjikov, Vladimir S. (ed.); Dimiev, Stancho (ed.) Trends in differential geometry, complex analysis and mathematical physics. Proceedings of 9th international workshop on complex structures, integrability and vector fields, Sofia, Bulgaria, August 25–29, 2008. (English) Zbl 1177.53007 Hackensack, NJ: World Scientific (ISBN 978-981-4277-71-6/hbk). xv, 273 p. (2009). MSC: 53-06 53Cxx 53Z05 81-06 00B25 PDFBibTeX XMLCite \textit{K. Sekigawa} (ed.) et al., Trends in differential geometry, complex analysis and mathematical physics. Proceedings of 9th international workshop on complex structures, integrability and vector fields, Sofia, Bulgaria, August 25--29, 2008. Hackensack, NJ: World Scientific (2009; Zbl 1177.53007)
Kostov, Nikolay A.; Gerdjikov, Vladimir S.; Valchev, Tihomir I. Bose-Fermi mixtures in two optical lattices. (English) Zbl 1193.35209 Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 224-240 (2008). MSC: 35Q55 35C07 76Y05 81V80 35C08 PDFBibTeX XMLCite \textit{N. A. Kostov} et al., in: Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 8--13, 2007. Sofia: Bulgarian Academy of Sciences. 224--240 (2008; Zbl 1193.35209)
Atanasov, V. A.; Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. Fordy-Kulish model and spinor Bose-Einstein condensate. (English) Zbl 1163.82006 J. Nonlinear Math. Phys. 15, No. 3, 291-298 (2008). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 82C10 82C26 35Q55 81U40 35Q51 35Q58 81Q05 PDFBibTeX XMLCite \textit{V. A. Atanasov} et al., J. Nonlinear Math. Phys. 15, No. 3, 291--298 (2008; Zbl 1163.82006) Full Text: DOI arXiv
Atanasov, Victor; Gerdjikov, Vladimir On the multi-component nonlinear Schrödinger equation with constant boundary conditions. (English) Zbl 1120.81022 Fiziev, Plamen P. (ed.) et al., Gravity, astrophysics and strings @ the Black Sea. Proceedings of the 3rd advanced research workshop, Kiten, Bulgaria, June 13–20, 2005. Sofia: St. Kliment Ohridski University Press (ISBN 978-954-07-2422-5/hbk). 22-36 (2006). MSC: 81Q05 81Q10 35Q55 81U15 PDFBibTeX XMLCite \textit{V. Atanasov} and \textit{V. Gerdjikov}, in: Gravity, astrophysics and strings \@ the Black Sea. Proceedings of the 3rd advanced research workshop, Kiten, Bulgaria, June 13--20, 2005. Sofia: St. Kliment Ohridski University Press. 22--36 (2006; Zbl 1120.81022)
Gerdjikov, Vladimir S.; Grahovski, Georgi G. On reductions and real Hamiltonian forms of affine Toda field theories. (English) Zbl 1105.37041 J. Nonlinear Math. Phys. 12, Suppl. 2, 153-168 (2005). Reviewer: Xianguo Geng (Zhengzhou) MSC: 37K30 37K60 81R12 37K05 PDFBibTeX XMLCite \textit{V. S. Gerdjikov} and \textit{G. G. Grahovski}, J. Nonlinear Math. Phys. 12, 153--168 (2005; Zbl 1105.37041) Full Text: DOI arXiv
Kostov, N. A.; Gerdjikov, V. S.; Enol’skii, V. Z.; Salerno, M.; Konotop, V. V. Two-component Bose-Einstein condensates in optical lattices. (English) Zbl 1099.35529 Abdullaev, Fatkhulla Kh. (ed.) et al., Nonlinear waves: Classical and quantum aspects. Proceedings of the NATO advanced research workshop, Estoril, Portugal, July 13-17, 2003. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-2189-5/pbk; 1-4020-2188-7/hbk). NATO Science Series II: Mathematics, Physics and Chemistry 153, 269-283 (2004). MSC: 35Q55 78A60 82D50 81V80 PDFBibTeX XMLCite \textit{N. A. Kostov} et al., NATO Sci. Ser. II, Math. Phys. Chem. 153, 269--283 (2004; Zbl 1099.35529)
Gerdjikov, V. S.; Kyuldjiev, A.; Marmo, G.; Vilasi, G. Construction of real forms of complexified Hamiltonian dynamical systems. (English) Zbl 1053.37031 Ablowitz, M. J. (ed.) et al., Nonlinear physics: theory and experiment II. Proceedings of the workshop, Gallipoli, Italy, June 27 – July 6, 2002. River Edge, NJ: World Scientific (ISBN 981-238-270-4). 172-178 (2003). MSC: 37J05 37J35 53D05 81R12 PDFBibTeX XMLCite \textit{V. S. Gerdjikov} et al., in: Nonlinear physics: theory and experiment II. Proceedings of the workshop, Gallipoli, Italy, June 27 -- July 6, 2002. River Edge, NJ: World Scientific. 172--178 (2003; Zbl 1053.37031)
Gerdjikov, V. S.; Grahovski, G. G.; Kostov, N. A. Reductions of \(N\)-wave interactions related to low-rank simple Lie algebras. I: \(\mathbb Z_2\)-reductions. (English) Zbl 1001.37074 J. Phys. A, Math. Gen. 34, No. 44, 9425-9461 (2001). Reviewer: Mircea Puta (Timişoara) MSC: 37K30 17B20 35A30 78A60 81U40 PDFBibTeX XMLCite \textit{V. S. Gerdjikov} et al., J. Phys. A, Math. Gen. 34, No. 44, 9425--9461 (2001; Zbl 1001.37074) Full Text: DOI arXiv
Gerdjikov, V. S.; Evstatiev, E. G.; Kaup, D. J.; Diankov, G. L.; Uzunov, I. M. Stability and quasi-equidistant propagation of NLS soliton trains. (English) Zbl 0948.81658 Phys. Lett., A 241, No. 6, 323-328 (1998). MSC: 81V10 37K40 37K10 PDFBibTeX XMLCite \textit{V. S. Gerdjikov} et al., Phys. Lett., A 241, No. 6, 323--328 (1998; Zbl 0948.81658) Full Text: DOI
Gerdjikov, V. S.; Kostov, N. A. Inverse scattering transform analysis of Stokes–anti-Stokes stimulated Raman scattering. (English) Zbl 0941.81608 Alfinito, E. (ed.) et al., Nonlinear physics: theory and experiment. Nature, structure and properties of nonlinear phenomena. Proceedings of the workshop, Lecce, Italy, June 29-July 7, 1995. Singapore: World Scientific. 489-492 (1996). MSC: 81V80 PDFBibTeX XMLCite \textit{V. S. Gerdjikov} and \textit{N. A. Kostov}, in: Nonlinear physics: theory and experiment. Nature, structure and properties of nonlinear phenomena. Proceedings of the workshop, Lecce, Italy, June 29--July 7, 1995. Singapore: World Scientific. 489--492 (1996; Zbl 0941.81608) Full Text: arXiv
Gerdjikov, V. S. \(Z_ N\)-reductions and new integrable versions of derivative nonlinear Schrödinger equations. (English) Zbl 0755.35129 Nonlinear evolution equations: integrability and spectral methods, Proc. Workshop, Como/Italy 1988, Proc. Nonlinear Sci., 367-372 (1990). MSC: 35Q55 37J35 37K10 81R10 17B81 PDFBibTeX XMLCite \textit{V. S. Gerdjikov}, in: Reduction of \(3 \times{} 3\) polynomial bundles and new types of integrable 3-wave interactions. . 367--372 (1990; Zbl 0755.35129)
Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I. Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil. (English) Zbl 0597.35112 J. Sov. Math. 34, 1923-1932 (1986). MSC: 35Q99 81U20 81Q05 PDFBibTeX XMLCite \textit{I. T. Gadzhiev} et al., J. Sov. Math. 34, 1923--1932 (1986; Zbl 0597.35112) Full Text: DOI
Gerdzhikov, V. S.; Kulish, P. P. Multicomponent nonlinear Schrödinger equation in the case of nonzero boundary conditions. (English) Zbl 0568.35084 J. Sov. Math. 30, 2261-2269 (1985). MSC: 35Q99 35J10 81U20 35P25 35R30 35A30 PDFBibTeX XMLCite \textit{V. S. Gerdzhikov} and \textit{P. P. Kulish}, J. Sov. Math. 30, 2261--2269 (1985; Zbl 0568.35084) Full Text: DOI
Gerdzhikov, V. S.; Kulish, P. P. On the multicomponent nonlinear Schrödinger equation in the case of non- vanishing boundary conditions. (Russian) Zbl 0522.35083 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 131, 34-46 (1983). MSC: 35Q99 35J10 81U20 35A30 35R30 35P25 PDFBibTeX XMLCite \textit{V. S. Gerdzhikov} and \textit{P. P. Kulish}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 131, 34--46 (1983; Zbl 0522.35083) Full Text: EuDML
Gerdzhikov, V. S.; Ivanov, M. I. The quadratic bundle of general form and the nonlinear evolution equations. II: Hierarchies of structures. (Russian) Zbl 0522.35082 Bulg. J. Phys. 10, 130-143 (1983). MSC: 35Q99 35P25 81U99 PDFBibTeX XMLCite \textit{V. S. Gerdzhikov} and \textit{M. I. Ivanov}, Bulg. J. Phys. 10, 130--143 (1983; Zbl 0522.35082)
Gerdzhikov, V. S.; Ivanov, M. I. The quadratic bundle of a general form and the nonlinear evolution equations. I: Expansions over the ”squared” solutions: generalized Fourier transform. (Russian) Zbl 0522.35081 Bulg. J. Phys. 10, 13-26 (1983). MSC: 35Q99 35P25 42A38 81U99 PDFBibTeX XMLCite \textit{V. S. Gerdzhikov} and \textit{M. I. Ivanov}, Bulg. J. Phys. 10, 13--26 (1983; Zbl 0522.35081)
Gadzhiev, I. T.; Gerdzhikov, V. S.; Ivanov, M. I. Hamiltonian structures of nonlinear evolution equations associated with a polynomial bundle. (Russian) Zbl 0514.35078 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 120, 55-68 (1982). MSC: 35Q99 81U20 81Q05 PDFBibTeX XMLCite \textit{I. T. Gadzhiev} et al., Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 120, 55--68 (1982; Zbl 0514.35078)