The general theory of discontinuities in nondissipative dispersive models had been developed. Discontinuity in this theory is any stationary transition between uniform, periodic, quasiperiodic or stohastic states. The theory includes the method of prediction of the type of discontinuity, observation of this discontinuity in numerical experiment, evolution condition analysis, methods to determine boundary conditions for the discontinuity, derivation and solution of averaged equations for wave zones, methods to obtain the shock structure as a solution of ordinary equation systems. One method is based on representation of shock structure as the special soliton-like solution, methods to obtain solitary or generalized solitary wave solution had been developed also.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1981 (department of hydromechanics), post-graduate in 1984. Ph.D. thesis was defended in 1985. D.Sci. thesis was defended in 2001. A list of my works contains more than 40 titles. I am a participant of A. G. Kulikovski and A. A. Barmin scientific school.
In 2000 I was awarded the prize for the best article in journal of Applied Mathematics and Mechanics.
Main publications:
Bakholdin I. B., Il'ichev A. T. Radiation and modulational instability described by the fifth-order Korteweg–de Vries equation // Contemporary Mathematics, 1996, v. 200, p. 1–15.
I. B. Bakholdin, “Study of discontinuity structures in solutions to the equations of a micropolar magnetoelastic medium taking into account the effects of a magnetic field and plasticity”, Zh. Vychisl. Mat. Mat. Fiz., 66:7 (2026), 1193–1206; Comput. Math. Math. Phys., 66:7 (2026), 1340–1353
2025
2.
I. B. Bakholdin, V. I. Erofeev, A. T. Il'ichev, “Spectral stability of subsonic solitary waves in an elastic electrically conductive micropolar medium”, Contin. Mech. Thermodyn., 37 (2025), 88–15
3.
I. B. Bakholdin, “Discontinuity structures in a micropolar magnetoelastic medium and methods for studying discontinuities in models with dispersion and a finite velocity of the wave propagation”, TMF, 224:3 (2025), 538–555; Theoret. and Math. Phys., 224:3 (2025), 1567–1581
I. B. Bakholdin, “Investigation of nondissipative discontinuity structures for equations of micropolar magnetoelastic medium and development of a general approach to the numerical solution of evolutionary partial differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 65:2 (2025), 180–192; Comput. Math. Math. Phys., 65:2 (2025), 359–371
I. B. Bakholdin, “Periodic and Solitary Waves and Nondissipative Discontinuity Structures in Electromagnetic Hydrodynamics in the Case of Wave Resonance”, Trudy Mat. Inst. Steklova, 322 (2023), 24–37; Proc. Steklov Inst. Math., 322 (2023), 18–31
8.
I. B. Bakholdin, “Discontinuity structures and solitary waves in electromagnetic hydrodynamics associated with linear and nonlinear Alfvén wave resonances”, Zh. Vychisl. Mat. Mat. Fiz., 63:11 (2023), 1894–1910; Comput. Math. Math. Phys., 63:11 (2023), 2123–2138
2022
9.
I. B. Bakholdin, A. T. Ilichev, “Fast magnetosonic solitonic structures in a quasi-neutral collision-free finite-beta plasma”, Wave Motion, 112 (2022), 102936–15
I. B. Bakholdin, “Nondissipative discontinuity structures and solitary waves in solutions to equations of two-fluid plasma in the electromagnetic hydrodynamics approximation”, Zh. Vychisl. Mat. Mat. Fiz., 62:12 (2022), 2090–2104; Comput. Math. Math. Phys., 62:12 (2022), 2139–2153
I. B. Bakholdin, “Analysis of two-fluid plasma in the electromagnetic hydrodynamics approximation and discontinuous structures in their solutions”, Zh. Vychisl. Mat. Mat. Fiz., 61:3 (2021), 458–474; Comput. Math. Math. Phys., 61:3 (2021), 436–452
I. B. Bakholdin, “Investigation of models that describe wave propagation in fluid-filled and gas-filled tubes with elastic walls”, Keldysh Institute preprints, 2017, 051, 32 pp.
2016
14.
I. B. Bakholdin, “Investigation of wave propagation in tubes with elastic walls and analysis of numerical methods”, Keldysh Institute preprints, 2016, 030, 32 pp.
15.
I. B. Bakholdin, A. V. Berezin, A. A. Kryukov, M. B. Markov, B. D. Plyushchenkov, D. N. Sadovnichii, “Electromagnetic wave in the medium with dispersion of dielectric permittivity”, Mat. Model., 28:8 (2016), 97–111; Math. Models Comput. Simul., 9:2 (2017), 190–200
I. B. Bakholdin, “Methods of investigation of wave propagation in fluid-filled tubes with elastic walls”, Keldysh Institute preprints, 2015, 070, 16 pp.
17.
I. B. Bakholdin, “Numerical study of solitary waves and reversible shock structures in tubes with controlled pressure”, Zh. Vychisl. Mat. Mat. Fiz., 55:11 (2015), 1921–1936; Comput. Math. Math. Phys., 55:11 (2015), 1884–1898
I. B. Bakholdin, “Methods of investigation of solitary waves and reversible shock structures in elastic tubes”, Keldysh Institute preprints, 2014, 073, 32 pp.
I. B. Bakholdin, “Methods of numerical analysis for investigation of reversible shock structures in media with complex dispersion”, Mat. Model., 26:11 (2014), 23–28
2013
20.
I. B. Bakholdin, “Methods of investigation, theory and classification of reversible shock structures in models of hydrodynamic type”, Keldysh Institute preprints, 2013, 030, 40 pp.
I. B. Bakholdin, E. R. Egorova, “Study of magnetosonic solitary waves for the electron magnetohydrodynamics equations”, Zh. Vychisl. Mat. Mat. Fiz., 51:3 (2011), 515–528; Comput. Math. Math. Phys., 51:3 (2011), 477–489
I. B. Bakholdin, “Methods of numerical investigation of magnetosonic solitary waves in plasma”, Keldysh Institute preprints, 2010, 038, 22 pp.
2009
23.
I. B. Bakholdin, “Low-dissipative shock structures with internal non-dissipative shocks”, Keldysh Institute preprints, 2009, 037, 32 pp.
2008
24.
I. B. Bakholdin, “Methods of analysis of resonance shock structures in low-dissipative media with dispersion”, Keldysh Institute preprints, 2008, 027, 26 pp.
2006
25.
I. B. Bakholdin, “Methods of analysis of multi-wave shock structures in low-dissipative models with dispersion”, Keldysh Institute preprints, 2006, 091, 30 pp.
2005
26.
I. B. Bakholdin, “Analysis methods for structures of dissipative and nondissipative jumps in dispersive systems”, Zh. Vychisl. Mat. Mat. Fiz., 45:2 (2005), 330–343; Comput. Math. Math. Phys., 45:2 (2005), 317–328
I. B. Bakholdin, V. Ya. Tomashpol'skii, “Solitary Waves in the Model of a Predeformed Nonlinear Composite”, Differ. Uravn., 40:4 (2004), 527–538; Differ. Equ., 40:4 (2004), 571–582
I. B. Bakholdin, “Nonstationary Solitary Wave Numerical Modeling”, Keldysh Institute preprints, 1997, 061
31.
I. B. Bakholdin, N. I. Kozlov, A. I. Kondrat'eva, “Numerical solution of Maxwell equations for action of electromagnetic pulse on human head”, Mat. Model., 9:8 (1997), 29–35
1996
32.
I. B. Bakholdin, “Investigation of Jumps and Solitary Waves in High-Order Dispersion Models”, Keldysh Institute preprints, 1996, 073
33.
I. B. Bakholdin, N. I. Kozlov, A. I. Kondrat'eva, “Numerical method of solution of Maxwell equations with jumps of electrophysical parameters of media”, Mat. Model., 8:4 (1996), 105–112
1994
34.
I. B. Bakholdin, N. I. Kozlov, A. I. Kondrat'eva, “Thin-slot formalism in three-dimensional computations of electromagnetic waves interaction with perfectly conductive solids”, Mat. Model., 6:8 (1994), 92–104
1993
35.
I. B. Bakholdin, N. I. Kozlov, A. I. Kondrat'eva, “The new algorithm of computing of three-dimensional Maxwell equations for system with several conductive solids of complicated form”, Mat. Model., 5:10 (1993), 91–95
1992
36.
I. B. Bakholdin, N. I. Kozlov, A. I. Kondrat'eva, “The method of computing of surface current and charge induced by electromagnetic field on solids of arbitrary form near earth surface”, Mat. Model., 4:5 (1992), 80–84
1991
37.
I. B. Bakholdin, N. I. Kozlov, A. I. Kondrat'eva, “The method of computing surface current and charge induced by electromagnetic field in free space on solids of arbitrary form”, Mat. Model., 3:5 (1991), 74–80
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