Department of Mathematical Sciences Loughborough University Tel: +44 (0) 1509 22 2861 Fax: +44 (0) 1509 22 3969

Karima Khusnutdinova

Journal publications (in reverse chronological order)

31. K.R. Khusnutdinova, K.R. Moore, Weakly nonlinear extension of d'Alembert's formula, IMA J. Appl. Math. (2012) in press.

30. K.R. Khusnutdinova, K.R. Moore, Initial-value problem for coupled Boussinesq equations and a hierarchy of Ostrovsky equations, Wave Motion 48 (2011) 738-752.

29. E.V. Ferapontov, K.R. Khusnutdinova and C. Klein, On linear degeneracy of integrable quasilinear systems in higher dimensions, Lett. Math. Phys. 96 (2011) 5-35.

28. G.V. Dreiden, A.M. Samsonov, I.V. Semenova, K.R. Khusnutdinova, Observation of a radiating bulk strain soliton in a solid waveguide, Techn. Physics 56 (2011) 889-892.

27. R.H.J. Grimshaw, K.R. Khusnutdinova, L.A. Ostrovsky, A.S. Topolnikov, Structure formation in the oceanic subsurface bubble layer by an internal wave field, Phys. Fluids 22 (2010) 106603.

26. G.V. Dreiden, K.R. Khusnutdinova, A.M. Samsonov, I.V. Semenova, Splitting induced generation of soliton trains in layered waveguides, J. Appl. Phys. 107 (2010) 034909 (featured in Scholarpedia article on "Solitons").

25. E.V. Ferapontov, L. Hadjikos and K.R. Khusnutdinova, Integrable equations of the dispersionless Hirota type and hypersurfaces in the Lagrangian Grassmannian, Int. Math. Res. Not. (2010) 496-535.

24. G.V. Dreiden, K.R. Khusnutdinova, A.M. Samsonov, I.V. Semenova, Longitudinal strain solitary wave in a two-layered polymeric bar, Strain 46 (2010) 589-598.

23. K.R. Khusnutdinova, A.M. Samsonov, A.S. Zakharov, Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures, Phys. Rev. E 79 (2009) 056606.

22. K.R. Khusnutdinova, A.M. Samsonov, A.S. Zakharov, Nonlinear long wave models for imperfectly bonded layered waveguides, Theor. Math. Phys. 159 (2009) 475-489.

21. G.V. Dreiden, K.R. Khusnutdinova, A.M. Samsonov, I.V. Semenova, Comparison of the effect of cyanoacrylate- and polyurethane- based adhesives on a longitudinal strain solitary wave in layered polymethylmethacrylate waveguides, J. Appl. Phys. 104 (2008) 086106.

20. K.R. Khusnutdinova, A.M. Samsonov, Fission of a longitudinal strain solitary wave in a delaminated bar, Phys. Rev. E 77 (2008) 066603 (featured in Scholarpedia article on "Solitons").

19. R.H.J. Grimshaw, K.R. Khusnutdinova and L.A. Ostrovsky, The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation, Eur. J. of Mech. - B/Fluids 27 (2008) 24-41.

18. K.R. Khusnutdinova, Coupled Klein-Gordon equations and energy exchange in two-component systems, EPJ Special Topics 147 (2007) 45-72 (invited review).

17. E.V. Ferapontov, K.R. Khusnutdinova, D.G. Marshall and M.V. Pavlov, Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt brackets, J. Math. Phys. 47 (2006) 103507 1-13.

16. E.V. Ferapontov and K.R. Khusnutdinova, The Haantjes tensor and double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability, Proc. Royal Soc. A 462 (2006) 1197-1219.

15. S.D. Griffiths, R.H.J. Grimshaw, K.R. Khusnutdinova, Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system, Physica D 214 (2006) 1 - 24.

14. E.V. Ferapontov, K.R. Khusnutdinova and S.P. Tsarev, On a class of three-dimensional integrable Lagrangians, Comm. Math. Phys. 261 (2006) 225-243.

13. E.V. Ferapontov, K.R. Khusnutdinova and M.V. Pavlov, Classification of integrable (2+1)-dimensional quasilinear hierarchies, Theor. Math. Phys. 144 (2005) 35-43.

12. R.H.J. Grimshaw, K.R. Khusnutdinova, Internal waves in a three-layer bubbly wavequide, Deep Sea Research II 51 (2004) 2905-2917.

11. E.V. Ferapontov, K.R. Khusnutdinova, Hydrodynamic reductions of multi-dimensional dispersionless PDEs: the test for integrability, J. Math. Phys. 45 (2004) 2365-2377.

10. R.H.J. Grimshaw, K.R. Khusnutdinova, The effect of bubbles on internal waves, J. Physical Oceanography 34 (2004) 477-489 (featured in March 2004 issue of Bull. Amer. Met. Soc.)

9. E.V. Ferapontov, K.R. Khusnutdinova, The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type, Physics A: Math. Gen. 37 (2004) 2949-2963.

8. E.V. Ferapontov, K.R. Khusnutdinova, On the integrability of (2+1)-dimensional quasilinear systems, Comm. Math. Phys. 248 (2004) 187-206.

7. S.D. Griffiths, R.H.J. Grimshaw, K.R. Khusnutdinova, The influence of modulational instability on energy exchange in coupled sine-Gordon equations, Theor. Math. Physics 137 (2003) 1448-1458.

6. K.R. Khusnutdinova, D.E. Pelinovsky, On the exchange of energy in coupled Klein-Gordon equations, Wave Motion 38 (2003) 1-10. (ERRATUM: an error in the derivation of coupled NLS equations (21) has been corrected in [8] above.)

5. K.R. Khusnutdinova, V.V. Silberschmidt, Lattice modelling of nonlinear waves in a bi-layer with delamination, Proc. Estonian Acad. Sci. Phys. Math. 52 (2003) 63-75.

4. K.R. Khusnutdinova, H. Steudel, Second harmonic generation: Hamiltonian structures and particular solutions, J. Math. Phys. 39 (1998) 3754-3764.

3. V.A. Baikov and K.R. Khusnutdinova, Formal linearization and exact solutions of some nonlinear partial differential equations, J. Nonlin. Math. Phys. 3 (1996) 139-146.

2. I.Sh. Akhatov, V.A. Baikov and K.R. Khusnutdinova, Nonlinear dynamics of coupled chains of particles, Prikl. Mat. Mekh. 59 (1995) No. 3, p. 376-384 (English transl. in J. Appl. Math. Mech. 59 (1995) 353-361).

1. K.R. Khusnutdinova, Nonlinear waves in a two-row system of particles, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1992) No. 2, 71-76 (in Russian).

Other refereed publications: books, proceedings, etc. (in reverse chronological order)

11. G. Dreiden, K. Khusnutdinova, A. Samsonov, I. Semenova, Nonlinear bulk strain waves in layered elastic waveguides with delamination: theory and experiments, XXII International Congress of Theoretical and Applied Mechanics, CD-ROM Proceedings, Adelaide, Australia, ISBN 978-0-9805142-1-6 (2008) 11385.

10. A. Samsonov, G. Dreiden, K. Khusnutdinova, and I. Semenova, Elastic Solitons in Delaminated Bars: Splitting Leads to Fission, Nonlinear Acoustics- Fundamentals and Applications, ISNA18, AIP Conference Proceedings, ed. B.O. Enflo, C.M. Hedberg, L. Kari, Stockholom, Sweden (2008) 307-310.

9. K.R. Khusnutdinova, Nonlinear waves in a bi-layer and coupled Klein-Gordon equations, Solid Mechanics and Its Applications, Volume 113, ed. A.B. Movchan, Kluwer Academic Publishers (2003) 537-546.

8. I.Sh. Akhatov, R.I. Nigmatulin, D.B. Khismatullin, and K.R. Khusnutdinova, Resonant interaction of long and short pressure waves in bubbly liquids, Proceedings of the Third International Conference on Multiphase Flow (ICMF'98), ed. J. Bataille, A. Joia, Lyon, France (1998), paper N 361, 8 pp.

7. K.R. Khusnutdinova, Exact solutions describing interaction of solitary waves of non-integrable equations, In ``Nonlinearity and Geometry'', Warsaw: PWN (1998) 319-333.

6. I.Sh. Akhatov, S.V. Belyutin, O.L. Kalyakina, D.B. Khismatullin, K.R. Khusnutdinova, One- and two-dimensional models of interaction of nonlinear waves in a bubbly medium, Acoustics of heterogeneous media (Dynamics of continuous media), Sibirian Branch of the Russian Academy of Sciences, Institute of Hydrodynamics, 112 (1997) 24-28 (in Russian).

5. I.Sh. Akhatov, S.V. Belyutin, D.B. Khismatullin, K.R. Khusnutdinova, Models of the nonlinear interaction of long and short waves in bubbly systems, Proceedings of the International Conference on ``Modern Problems of Mathematics and Mechanics'', V.1, Moscow: Lomonosov Moscow State University (1997) 34-37 (in Russian).

4. K.R. Khusnutdinova, Mathematical methods of nonlinear mechanics, Ufa: Bashkir State University (1996) 82 pp. (Book - short work, in Russian).

3. I.Sh. Akhatov, S.V. Belyutin, D.B. Khismatullin, K.R. Khusnutdinova, On the interaction of long and short waves in bubbly systems, Proceedings of the conference on applied mechanics, Ufa: Bashkir State University (1996) 154-156 (in Russian).

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

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

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