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Loughborough University Research Publications


Publications for Karima Khusnutdinova

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Journal Articles

Hooper, CG, Ruiz, PD, Huntley, JM, Khusnutdinova, KR (2021) Undular Bores Generated by Fracture, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, ISSN: 1539-3755. DOI: 10.1103/PhysRevE.104.044207.

Hooper, C, Khusnutdinova, K, Grimshaw, R (2021) Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current, Journal of Fluid Mechanics, 927, pp.A37-1-A37-39, ISSN: 0022-1120. DOI: 10.1017/jfm.2021.787.

Khusnutdinova, K (2020) Long internal ring waves in a two-layer fluid with an upper-layer current, Russian Journal of Earth Sciences, 20, ES4006, ISSN: 1681-1208. DOI: 10.2205/2020ES000734.

Garbuzov, FE, Beltukov, YM, Khusnutdinova, KR (2020) Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and Cubic nonlinearities, Theoretical and Mathematical Physics(Russian Federation), 202(3), pp.319-333, ISSN: 0040-5779. DOI: 10.1134/S0040577920030046.

Khusnutdinova, K, Fu, Y, Grimshaw, R, Pastrone, F (2020) Special issue of Wave Motion - “Nonlinear waves in solids: In memory of Alexander M. Samsonov”, Wave Motion, 92, pp.102379-102379, ISSN: 0165-2125. DOI: 10.1016/j.wavemoti.2019.102379.

Khusnutdinova, KR and Pelinovsky, DE (2019) Preface: Nonlinear waves in fluids in honor of Roger Grimshaw on the occasion of his 80th birthday: Part II, Studies in Applied Mathematics, 142(4), pp.417-418, ISSN: 0022-2526. DOI: 10.1111/sapm.12267.

Khusnutdinova, KR and Tranter, MR (2019) D'Alembert-type solution of the Cauchy problem for the Boussinesq-Klein-Gordon equation, Studies in Applied Mathematics, 142(4), pp.551-585, ISSN: 0022-2526. DOI: 10.1111/sapm.12263.

Khusnutdinova, KR and Pelinovsky, DE (2019) Preface: Nonlinear waves in fluids in honor of Roger Grimshaw on the occasion of his 80th birthday, Studies in Applied Mathematics, 142(3), pp.215-218, ISSN: 0022-2526. DOI: 10.1111/sapm.12262.

Garbuzov, FE, Khusnutdinova, K, Semenova, IV (2019) On Boussinesq-type models for long longitudinal waves in elastic rods, Wave Motion, 88, pp.129-143, ISSN: 0165-2125. DOI: 10.1016/j.wavemoti.2019.02.004.

Khusnutdinova, KR, Stepanyants, YA, Tranter, MR (2018) Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves, Physics of Fluids, 30(2), pp.022104-022104, ISSN: 1070-6631. DOI: 10.1063/1.5009965.

Grimshaw, RHJ, Khusnutdinova, KR, Moore, KR (2017) Radiating solitary waves in coupled Boussinesq equations, IMA Journal of Applied Mathematics, 82(4), pp.802-820, ISSN: 0272-4960. DOI: 10.1093/imamat/hxx014.

Khusnutdinova, KR and Tranter, MR (2017) On radiating solitary waves in bi-layers with delamination and coupled Ostrovsky equations, Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(1), pp.013112-013112, ISSN: 1054-1500. DOI: 10.1063/1.4973854.

Khusnutdinova, KR and Zhang, X (2016) Nonlinear ring waves in a two-layer fluid, Physica D: Nonlinear Phenomena, 333, pp.208-221, ISSN: 0167-2789. DOI: 10.1016/j.physd.2016.02.013.

Khusnutdinova, KR and Zhang, X (2016) Long ring waves in a stratified fluid over a shear flow, Journal of Fluid Mechanics, 794, pp.17-44, ISSN: 0022-1120. DOI: 10.1017/jfm.2016.147.

Khusnutdinova, KR and Tranter, MR (2015) Modelling of nonlinear wave scattering in a delaminated elastic bar, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2183), pp.20150584-20150584, ISSN: 1364-5021. DOI: 10.1098/rspa.2015.0584.

Khusnutdinova, K (2015) Nonlinear waves in integrable and nonintegrable systems (Mathematical Modeling and Computation 16)ByJianke Yang, Bulletin of the London Mathematical Society, 47(1), pp.188-190, ISSN: 0024-6093. DOI: 10.1112/blms/bdu100.

Alias, A, Grimshaw, RHJ, Khusnutdinova, KR (2014) Coupled Ostrovsky equations for internal waves in a shear flow, Physics of Fluids, 26(12), pp.126603-126603, ISSN: 1070-6631. DOI: 10.1063/1.4903279.

Khusnutdinova, KR, Moore, KR, Pelinovsky, DE (2014) Validity of the weakly nonlinear solution of the cauchy problem for the boussinesq-type equation, Studies in Applied Mathematics, 133(1), pp.52-83, ISSN: 0022-2526. DOI: 10.1111/sapm.12034.

Alias, A, Grimshaw, RHJ, Khusnutdinova, KR (2014) Coupled Ostrovsky Equations for Internal Waves, with a Background Shear Flow, Procedia IUTAM, 11, pp.3-14, ISSN: 2210-9838. DOI: 10.1016/j.piutam.2014.01.043.

Alias, A, Grimshaw, RHJ, Khusnutdinova, KR (2013) On strongly interacting internal waves in a rotating ocean and coupled Ostrovsky equations, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(2), pp.023121-023121, ISSN: 1054-1500. DOI: 10.1063/1.4808249.

Khusnutdinova, KR, Klein, C, Matveev, VB, Smirnov, AO (2013) On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(1), pp.013126-013126, ISSN: 1054-1500. DOI: 10.1063/1.4792268.

Dreiden, GV, Khusnutdinova, KR, Samsonov, AM, Semenova, IV (2012) Bulk strain solitary waves in bonded layered polymeric bars with delamination, Journal of Applied Physics, 112(6), pp.063516-063516, ISSN: 0021-8979. DOI: 10.1063/1.4752713.

Khusnutdinova, KR and Moore, KR (2012) Weakly non-linear extension of d'Alembert's formula, IMA Journal of Applied Mathematics, 77(3), pp.361-381, ISSN: 0272-4960. DOI: 10.1093/imamat/hxs034.

Khusnutdinova, KR and Moore, KR (2011) Initial-value problem for coupled Boussinesq equations and a hierarchy of Ostrovsky equations, WAVE MOTION, 48(8), pp.738-752, ISSN: 0165-2125. DOI: 10.1016/j.wavemoti.2011.04.003.

Ferapontov, EV, Khusnutdinova, KR, Klein, C (2011) On Linear Degeneracy of Integrable Quasilinear Systems in Higher Dimensions, Letters in Mathematical Physics, 96(1-3), pp.5-35, ISSN: 0377-9017. DOI: 10.1007/s11005-011-0462-4.

Dreiden, GV, Samsonov, AM, Semenova, IV, Khusnutdinova, KR (2011) Observation of a radiating bulk strain solitary wave in a layered solid waveguide, Techn. Physics, 56, pp.889-892.

Dreiden, GV, Khusnutdinova, KR, Samsonov, AM, Semenova, IV (2010) Longitudinal Strain Solitary Wave in a Two-Layered Polymeric Bar, Strain, 46(6), pp.589-598, ISSN: 0039-2103. DOI: 10.1111/j.1475-1305.2008.00471.x.

Grimshaw, RHJ, Khusnutdinova, KR, Ostrovsky, LA, Topolnikov, AS (2010) Structure formation in the oceanic subsurface bubble layer by an internal wave field, Physics of Fluids, 22(10), pp.106603-106603, ISSN: 1070-6631. DOI: 10.1063/1.3499379.

Dreiden, GV, Khusnutdinova, KR, Samsonov, AM, Semenova, IV (2010) Splitting induced generation of soliton trains in layered waveguides, Journal of Applied Physics, 107(3), pp.034909-034909, ISSN: 0021-8979. DOI: 10.1063/1.3294612.

Ferapontov, EV, Hadjikos, L, Khusnutdinova, KR (2010) Integrable Equations of the Dispersionless Hirota type and Hypersurfaces in the Lagrangian Grassmannian, International Mathematics Research Notices, 2010(3), pp.496-535, ISSN: 1073-7928. DOI: 10.1093/imrn/rnp134.

Khusnutdinova, KR, Samsonov, AM, Zakharov, AS (2009) Nonlinear long-wave models for imperfectly bonded layered waveguides, Theoretical and Mathematical Physics, 159(3), pp.819-832, ISSN: 0040-5779. DOI: 10.1007/s11232-009-0070-y.

Khusnutdinova, KR, Samsonov, AM, Zakharov, AS (2009) Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures, Physical Review E, 79(5), 056606, ISSN: 1539-3755. DOI: 10.1103/physreve.79.056606.

Dreiden, GV, Khusnutdinova, KR, Samsonov, AM, Semenova, IV (2008) Comparison of the effect of cyanoacrylate- and polyurethane-based adhesives on a longitudinal strain solitary wave in layered polymethylmethacrylate waveguides, Journal of Applied Physics, 104(8), pp.086106-086106, ISSN: 0021-8979. DOI: 10.1063/1.3000665.

Khusnutdinova, KR and Samsonov, AM (2008) Fission of a longitudinal strain solitary wave in a delaminated bar, Physical Review E, 77(6), 066603, ISSN: 1539-3755. DOI: 10.1103/physreve.77.066603.

Grimshaw, RHJ, Khusnutdinova, KR, Ostrovsky, LA (2008) The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation, European Journal of Mechanics - B/Fluids, 27(1), pp.24-41, ISSN: 0997-7546. DOI: 10.1016/j.euromechflu.2007.03.002.

Khusnutdinova, KR (2007) Coupled Klein–Gordon equations and energy exchange in two-component systems, The European Physical Journal Special Topics, 147(1), pp.45-72, ISSN: 1951-6355. DOI: 10.1140/epjst/e2007-00202-0.

Ferapontov, EV, Khusnutdinova, KR, Marshall, DG, Pavlov, MV (2006) Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt’s brackets, Journal of Mathematical Physics, 47(10), pp.103507-103507, ISSN: 0022-2488. DOI: 10.1063/1.2354590.

Ferapontov, EV and Khusnutdinova, KR (2006) The Haantjes tensor and double waves for multi-dimensional systems of hydrodynamic type: a necessary condition for integrability, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 462(2068), pp.1197-1219, ISSN: 1364-5021. DOI: 10.1098/rspa.2005.1627.

Griffiths, SD, Grimshaw, RHJ, Khusnutdinova, KR (2006) Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system, Physica D: Nonlinear Phenomena, 214(1), pp.1-24, ISSN: 0167-2789. DOI: 10.1016/j.physd.2005.11.011.

Ferapontov, EV, Khusnutdinova, KR, Tsarev, SP (2006) On a Class of Three-Dimensional Integrable Lagrangians, Communications in Mathematical Physics, 261(1), pp.225-243, ISSN: 0010-3616. DOI: 10.1007/s00220-005-1415-5.

Ferapontov, EV, Khusnutdinova, KR, Pavlov, MV (2005) Classification of Integrable (2+1)-Dimensional Quasilinear Hierarchies, Theoretical and Mathematical Physics, 144(1), pp.907-915, ISSN: 0040-5779. DOI: 10.1007/s11232-005-0117-7.

Grimshaw, RHJ and Khusnutdinova, KR (2004) Internal waves in a three-layer bubbly waveguide, Deep Sea Research Part II: Topical Studies in Oceanography, 51(25-26), pp.2905-2917, ISSN: 0967-0645. DOI: 10.1016/j.dsr2.2004.09.003.

Ferapontov, EV and Khusnutdinova, KR (2004) On the Integrability of (2+1)-Dimensional Quasilinear Systems, Communications in Mathematical Physics, 248(1), pp.187-206, ISSN: 0010-3616. DOI: 10.1007/s00220-004-1079-6.

Ferapontov, EV and Khusnutdinova, KR (2004) Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability, Journal of Mathematical Physics, 45(6), pp.2365-2377, ISSN: 0022-2488. DOI: 10.1063/1.1738951.

Ferapontov, EV and Khusnutdinova, KR (2004) The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type, Journal of Physics A: Mathematical and General, 37(8), pp.2949-2963, ISSN: 0305-4470. DOI: 10.1088/0305-4470/37/8/007.

Grimshaw, RHJ and Khusnutdinova, KR (2004) The Effect of Bubbles on Internal Waves, Journal of Physical Oceanography, 34(2), pp.477-489, ISSN: 0022-3670. DOI: 10.1175/1520-0485(2004)034<0477:teoboi>2.0.co;2.

Griffiths, SD, Grimshaw, RHJ, Khusnutdinova, KR (2003) The influence of modulational instability on energy exchange in coupled sine-Gordon equations, Theoretical and Mathematical Physics, 137(1), pp.1448-1458, ISSN: 0040-5779. DOI: 10.1023/A:1026008907682.

Khusnutdinova, KR and Pelinovsky, DE (2003) On the exchange of energy in coupled Klein–Gordon equations, Wave Motion, 38(1), pp.1-10, ISSN: 0165-2125. DOI: 10.1016/s0165-2125(03)00022-2.

Khusnutdinova, KR and Silberschmidt, VV (2003) Lattice modelling of nonlinear waves in a bi-layer with delamination, Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 52(1), pp.63-75, ISSN: 1406-0086.

Khusnutdinova, KR and Steudel, H (1998) Second harmonic generation: Hamiltonian structures and particular solutions, Journal of Mathematical Physics, 39(7), pp.3754-3764, ISSN: 0022-2488. DOI: 10.1063/1.532465.

Lopatin, AK (1996) Symmetry in Nonlinear Mechanics: Averaging and Normalization Procedures, New Problems and Algorithms, Journal of Nonlinear Mathematical Physics, 3(1-2), pp.111-111, DOI: 10.2991/jnmp.1996.3.1-2.13.

Akhatov, IS, Baikov, VA, Khusnutdinova, KR (1995) Non-linear dynamics of coupled chains of particles, Journal of Applied Mathematics and Mechanics, 59(3), pp.353-361, ISSN: 0021-8928. DOI: 10.1016/0021-8928(95)00042-n.

Khusnutdinova, KR (1992) Nonlinear waves in a double row particle system, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (in Russian), 2, pp.71-76.



Conferences

Hooper, C, Ruiz, P, Khusnutdinova, K, Huntley, JM (2019) An experimental and theoretical study of longitudinal bulk strain waves generated by fracture. In 14th International Conference on Advances in Experimental Mechanics, Belfast, Ireland.

Khusnutdinova, K and Tranter, M (2017) Scattering of bulk strain solitary waves in bi-layers with delamination. In X International Conference on Structural Dynamics, EURODYN 2017, Rome, Italy, pp.1533-1538, DOI: 10.1016/j.proeng.2017.09.497.

Khusnutdinova, K (2012) R. Grimshaw, L.A. Ostrovsky, A.S. Topolnikov, K.R. Khusnutdinova, Dynamics of the bubble layer close to the ocean surface under the existence of an internal wave and Langmuir curculations. In Proceedings of the Institute of Mechanics of the Ufa Scientific Centre of the RAS, ISBN 978-5-98755-116-7, Ufa, Russia, pp.76-81.

Khusnutdinova, K (2012) I.V. Semenova, G.V. Dreiden, K.R. Khusnutdinova, A.M. Samsonov, Holographic approach to detection of delamination areas in layered polymeric waveguides by means of strain solitons,. In Optical Metrology and Inspection for Industrial Applications II, Proc. of SPIE, pp.85630V1-85630V11, DOI: 10.1117/12.999709.

Khusnutdinova, K (2011) A.S. Topolnikov, K.R. Khusnutdinova, L.A. Ostrovsky, R. Grimshaw, Modelling dynamics of the oceanic subsurface bubble layer under the action of an internal wave. In In "Fundamental Problems of Theoretical and Applied Mechanics", Vestnik of Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia, pp.2526-2527.

Khusnutdinova, K (2011) R. Grimshaw, L.A. Ostrovsky, A.S. Topolnikov, K.R. Khusnutdinova, The effect of an internal wave on the propagation of sound in the subsurface bubble layer. In Proceedings of the Institute of Mechanics of the Ufa Scientific Centre of the RAS, ISBN 978-5-905220-05-0, Ufa, pp.54-64.

Samsonov, AM, Dreiden, G, Khusnutdinova, KR, Semenova, I (2008) Elastic Solitons in Delaminated Bars:Splitting Leads to Fisson. In Enflo, BO, Hedberg, CM, eds, LK (ed) AIP Conference Proceedings, Nonlinear Acoustics - Fundamentals and Applications, Stockholm, Sweden, pp.307-310.

Dreiden, G, Khusnutdinova, KR, Samsonov, AM, Semenova, I (2008) Nonlinear bulk strain waves in layered elastic waveguides with delamination: theory and experiments. In CD-ROM Proceedings, XXII International Congress of Theoretical and Applied Mechanics, Adelaide, Australia, Art No. 11385, ISBN: 978-0-9805142-1-6.

Khusnutdinova, KR (2003) Nonlinear waves in a bi-layer and coupled Klein-Gordon equations, Solid Mechanics and Its Applications. In ed, ABM (ed) Asymptotics, Singularities and Homogenization in Problems of Mechanics, Dordrecht, pp.537-546.

Akhatov, IS, Nigmatulin, RI, Khismatullin, DB, Khusnutdinova, KR (1998) Resonant interaction of long and short pressure waves in bubbly liquids. In Bataille, J and eds, AJ (ed) Proceedings of the Third International Conference on Multiphase Flow (ICMF'98), Lyon, France, Art.No. 361.

Khusnutdinova, KR (1998) Exact solutions describing interaction of solitary waves of non-integrable equations. In Nonlinearity and Geometry, Warsaw: PWN, pp.319-333.

Akhatov, IS, Belyutin, SV, Khismatullin, DB, Khusnutdinova, KR (1997) Models of the nonlinear interaction of long and short waves in bubbly systems. In Modern Problems of Mathematics and Mechanics. (in Russian), Processings of the International Conference, V.1, Moscow: Lomonosov Moscow State University, pp.34-37.

Akhatov, IS, Belyutin, SV, Kalyakina, OL, Khismatullin, DB, Khusnutdinova, KR (1997) One-and two-dimensional models of interaction of nonlinear waves in a bubbly medium. In Sibirian Branch of the Russian Academy of Sciences, In "Acoustics of heterogeneous media (Dynamics of continuous media)". (in Russian), Institute of Hydrodynamics, pp.24-28.

Akhatov, IS, Belyutin, SV, Khismatullin, DB, Khusnutdinova, K (1996) On the interaction of long and short waves in bubbly systems. In Ufa: (in Russian), Proceedings of the conference on applied mechanics, Bashkir State University, pp.154-156.

Khusnutdinova, KR (1993) Wave dynamics of a medium constructed on the basis of a double row particle system. In V.2, Moscow: (in Russian), Deep refinement of hydrocarbon material, TsNIITEneftekhim, pp.136-145.

Khusnutdinova, KR (1993) Group classification of the equations of motion of connected chains of particles. In Saratov. Univ. (in Russian), Modern Group Analysis and Problems of Mathematical Modelling, Samar. Filial, Samara, pp.181-186.



Chapters

Khusnutdinova, K and Tranter, M (2019) Nonlinear longitudinal bulk strain waves in layered elastic waveguides. In Berezovski, A and Soomere, T (ed) Applied Wave Mathematics II: Selected Topics in Solids, Fluids, and Mathematical Methods and Complexity, Springer, pp.125-150, ISBN: 9783030299507. DOI: 10.1007/978-3-030-29951-4_6.

Khusnutdinova, KR and Tranter, MR (2019) Weakly-nonlinear solution of coupled Boussinesq equations and radiating solitary waves. In Altenbach, H (ed) Dynamical processes in Generalised Continua and Structures. Series: Advanced Structured Materials, 103, Springer, pp.321-344.

Khusnutdinova, K (1996) Mathematical methods of nonlinear mechanics. In Mathematical methods of nonlinear mechanics, Ufa: (in Russian).



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