Publications

  1. H.A Erbay and S. Erbay, “On the propagation of acceleration waves in circular cylindrical elastic membrane tubes subjected to axial extension”,  Journal of Elasticity 158, 26 (2026). https://doi.org/10.1007/s10659-026-10202-7 
  2. H. Borluk, H.A. Erbay, S. Erbay and A. Erkip, “On the relevance of the Rosenau-type equations for nonlinear wave propagation in one-dimensional lattices”, Applicable Analysis  (2026). https://doi.org/10.1080/00036811.2026.2646611
  3. H.A. Erbay and S. Erbay, “Traveling wave  solutions of the doubly regularized nonlinear Boussinesq equation”, Chaos, Solitons & Fractals 206, 117967 (2026). https://doi.org/10.1016/j.chaos.2026.117967
  4. H.A. Erbay, S. Erbay and A. Erkip, “Convergence of  a linearly regularized nonlinear wave equation to the p-system”, Turkish Journal of Mathematics 47, 1003-1014 (2023).  https://doi.org/10.55730/1300-0098.3407
  5. H.A. Erbay, S. Erbay and A. Erkip, “A comparison of solutions of two convolution-type unidirectional wave equations”, Applicable Analysis 102, 4422-4431 (2022). https://doi.org/10.1080/00036811.2022.2118117
  6. H.A. Erbay, S. Erbay and A. Erkip, “On the full dispersion Kadomtsev-Petviashvili equations for dispersive elastic waves”, Wave Motion 114, 103015 (2022). https://doi.org/10.1016/j.wavemoti.2022.103015
  7. H.A. Erbay, S. Erbay and A. Erkip, “A semi-discrete numerical scheme for nonlocally regularized KdV-type equations”, Applied Numerical Mathematics 175, 29-39 (2022). https://doi.org/10.1016/j.apnum.2022.02.003
  8. H.A. Erbay, S. Erbay and A. Erkip, “On the convergence of the nonlocal nonlinear model to the classical elasticity equation” , Physica:D Nonlinear Phenomena 427,133010 (2021). https://doi.org/10.1016/j.physd.2021.133010
  9. H.A. Erbay, S. Erbay and A. Erkip, “A semi-discrete numerical method for convolution-type unidirectional wave equations“, Journal of Computational and Applied Mathematics  387, 112496 (2021).
  10. H.A. Erbay, S. Erbay and A. Erkip, “Numerical computation of solitary wave solutions of the Rosenau equation“, Wave Motion 98,  102618 (2020). https://doi.org/10.1016/j.wavemoti.2020.102618
  11. H.A. Erbay, S. Erbay and A. Erkip, “Comparison of nonlocal nonlinear wave equations in the long-wave limit“, Applicable Analysis 99, 2670-2679 (2020).
  12. H.A. Erbay, S. Erbay and A. Erkip, “Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations“, Discrete and Continuous Dynamical Systems 39, 2877-2891 (2019).
  13. H.A. Erbay, S. Erbay and A. Erkip, “Convergence of a semi-discrete numerical method for a class of nonlocal nonlinear wave equations“, ESAIM: Mathematical Modelling and Numerical Analysis 52, 803-826 (2018).
  14. H.A. Erbay, S. Erbay and A. Erkip, “On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations“, Discrete and Continuous Dynamical Systems 37, 3111-3122 (2017).
  15. H.A. Erbay, S. Erbay and A. Erkip, “Derivation of generalized Camassa-Holm equations from Boussinesq-type equations“, Journal of Nonlinear Mathematical Physics 23, 314-322 (2016).
  16. H.A. Erbay, S. Erbay and A. Erkip, “The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations“, Discrete and Continuous Dynamical Systems 36, 6101-6116 (2016)
  17. H.A. Erbay, S. Erbay and A. Erkip, “Instability and stability properties of traveling waves for the double dispersion equation“, Nonlinear Analysis: Theory, Methods & Applications 133, 1-14 (2016).
  18. H.A. Erbay, S. Erbay and A. Erkip, “Some remarks on  the stability and instability  properties of solitary waves for the double dispersion equation“, Proceedings of the Estonian Academy of Sciences 64, 263-269 (2015).
  19. H.A. Erbay, S. Erbay and A. Erkip, “Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: The KdV, BBM and CH equations“, Proceedings of the Estonian Academy of Sciences 64, 256-262 (2015).
  20. H.A. Erbay, S. Erbay and A. Erkip, “Derivation of the Camassa-Holm equations for elastic waves“, Physics Letters A  379, 956-961 (2015).
  21. H.A. Erbay, S. Erbay and A. Erkip, “Existence and Stability of Traveling Waves for a Class of Nonlocal Nonlinear Equations“,  Journal of Mathematical Analysis and Applications 425, 307-336 (2015).
  22. H.A. Erbay, S. Erbay and A. Erkip, “Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations“, Nonlinear Analysis: Theory, Methods & Applications 95, 313-322 (2014).
  23. H.A. Erbay and S. Erbay, “Transverse linear instability of solitary waves for coupled long-wave-short-wave interaction equations“, Applied Mathematics Letters 25, 2402-2406 (2012).
  24. H.A. Erbay, S. Erbay and A. Erkip, “The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials”, Nonlinearity 24, 1347-1359 (2011).
  25. H. Borluk, S. Erbay, Stability of solitary waves for three-coupled long wave–short wave interaction equations, IMA Journal of Applied Mathematics 76, 582-598 (2011).
  26. H. Borluk, H. A. Erbay and S. Erbay, “Non-existence and existence of localized solitary waves for the two-dimensional long-wave-short-wave interaction equations“,Applied Mathematics Letters 23, 356-360 (2010).
  27. A. Eden, S. Erbay, I. Hacinliyan, “Reducing a generalized Davey-Stewartson system to non-local nonlinear Schrödinger equation”, Chaos, Soliton and Fractals 41, 688-697 (2009).
  28.  A. Eden, S. Erbay, “Standing waves for a generalized Davey- Stewartson system”, Journal of Physics A: Mathematical and General 39, 13435-44 (2006).
  29. A. Eden, S. Erbay, “On travelling wave solutions of a generalized Davey- Stewartson system”, IMA Journal of Applied Mathematic. 70, 15-24 (2005).
  30. C. Babaoglu, A. Eden, S. Erbay, “Global existence and nonexistence results for a generalized Davey-Stewartson equation” Journal of Physics A: Mathematical and General 37, 11531-11546 (2004).
  31. I. Hacinliyan, S. Erbay, “Coupled quintic nonlinear Schrödinger equations in a generalized elastic solid”, Journal of Physics A: Mathematical and Genera. 37, 9387- 9401 (2004).
  32. C. Babaoglu, S. Erbay, “Two-dimensional wave packets in an elastic solid with couple stresses”, International Journal of Non-Linear Mechanics 39, 941-949 (2004).
  33. I. Hacinliyan, S.Erbay, “A higher-order model for transverse waves in a generalized elastic solid”, Chaos, Solitons and Fractals 14, 1127-1135 (2002).
  34. C. Babaoglu, S. Erbay, “Two-dimensional wave propagation in a generalized elastic solid”, Chaos, Solitons and Fractals 12, 381-389 (2001).
  35. S. Erbay, “Nonlinear interaction between long and short waves in a generalized elastic solid”, Chaos, Solitons and Fractals 11, 1789-1798 (2000).
  36. S. Erbay, “Coupled modified Kadomtsev-Petviashvili equations in dispersive elastic media”, International Journal of Non-Linear Mechanics 34, 289-297 (1999).
  37. H.A. Erbay and S. Erbay, “Four-wave interaction equations: Hamiltonian formulation, conservation laws and Hirota method“, J. Phys. A: Math. Gen. 29, 77-85, (1996).
  38. S. Erbay, “Modulation of waves near the marginal state of instability in fluid-filled distensible tubes Journal of Physics A: Mathematical and General 28, 2905-2919 (1995).
  39. H.A. Erbay and S. Erbay, “Nonlinear interaction of transverse acoustical and optical waves in micropolar elastic media“, International Journal of Non-Linear Mechanics29, 163-176, (1994).
  40. S. Erbay and H. A. Erbay, “Nonlinear wave modulation in fluid filled distensible tubes“, Acta Mechanica 104, 201-214, (1994).
  41. H.A. Erbay, S. Erbay, N. Djilali and S. Dost, “Numerical simulation of dissolution and liquid–phase–epitaxial growth of silicon“, Computational Fluid Dynamics Journal 2, 227-243, (1993).
  42. S. Erbay, H.A. Erbay, N. Djilali and S. Dost, “Investigation of solutal convection during the dissolution of silicon in a sandwich system“, International Journal of Heat and Mass Transfer 36, 3017-3027, (1993).
  43. H.A. Erbay, S. Erbay and S. Dost, “Wave propagation in fluid-filled nonlinear viscoelastic tubes“, Acta Mechanica 95, 87-102, (1992).
  44. S. Erbay, H.A. Erbay and S. Dost, “Nonlinear wave interactions in a micropolar elastic medium“, Wave Motion 16, 163-172, (1992).
  45. S. Erbay, H.A. Erbay and S. Dost, “Nonlinear wave modulation in micropolar elastic media-I. Longitudinal waves“, International Journal of Engineering Science 29, 845-858, (1991).
  46. H.A. Erbay, S. Erbay and S. Dost, “Nonlinear wave modulation in micropolar elastic media-II. Transverse waves“, International Journal of Engineering Science 29, 859-868, (1991).
  47. H.A. Erbay, S. Erbay and S. Dost, “Thermally induced vibrations in a generalized thermoelastic solid with a cavity“, Journal of Thermal Stresses 14, 161-171, (1991).
  48. S. Erbay, E.S. Suhubi, “Nonlinear wave propagation in micropolar media–I. The general theory”, International Journal of Engineering Science 27, 895-914 (1989).
  49. S.Erbay, E.S. Suhubi, “Nonlinear wave propagation in micropolar media–II. Special cases, solitary waves and Painleve analysis”, International Journal of Engineering Science 27, 915-919 (1989).
  50. H. Demiray, H.A. Erbay and S. Erbay, “Effect of prestress on pulse waves in arteries“,Z. angew. Math. Mech.(ZAMM) 67, 473-485, (1987).
  51. H.A. Erbay, S. Erbay and H. Demiray, “Pulse waves in prestressed arteries “, Bulletin of Mathematical Biology 49, 289-305, (1987).
  52. S. Erbay, E.S. Suhubi, “Longitudinal wave propagation in a generalized  thermoelastic cylinder”, Journal of Thermal Stresses 9, 279-295 (1986).
  53. S. Erbay, O. Oguz, “A super extension of WKI integrable systems”, Journal of Physics A: Mathematical and General 18, L969-L974 (1985).