Publications

Journal Articles

  1. H.A. ERBAY, S. Erbay and A. Erkip, “On  the  convergence  of   the   nonlocal  nonlinear model to the classical elasticity equation” (submitted).
  2. H.A. ERBAY, S. Erbay and A. Erkip, “Numerical computation of solitary wave solutions of the Rosenau equation“, Wave Motion 98, Article number: 102618 (2020).
  3. H.A. ERBAY,  A. Erkip and Y. Şengül, “Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity“, Journal of Differential Equations 269, 9720-9739 (2020).
  4. H.A. ERBAY and Y. Şengül, “A thermodynamically consistent stress-rate type model of one dimensional strain-limiting viscoelasticity“,   Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP)  71, Article number: 94 (2020).
  5. 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 (2019) 112496, https://doi.org/10.1016/j.cam.2019.112496.
  6. H.A. ERBAY, S. Erbay and A. Erkip, “Comparison of nonlocal nonlinear wave equations in the long-wave limit“,  Applicable Analysis 99, 2668–2677 (2020).
  7. 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).
  8. 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).
  9. 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).
  10. 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).
  11. 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).
  12. 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).
  13.  H.A. ERBAY and Y. Şengül, “Traveling waves in one-dimensional nonlinear models of strain-limiting viscoelasticity“, International Journal of Non-Linear Mechanics 77, 61-68 (2015).
  14. 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).
  15. 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).
  16. H.A. ERBAY, S. Erbay and A. Erkip, “Derivation of the Camassa-Holm equations for elastic waves“, Physics Letters A  379, 956-961 (2015).
  17. 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).
  18. 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).
  19. C. Babaoglu, H.A. ERBAY and A. Erkip, “Global existence and blow-up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations“, Nonlinear Analysis: Theory, Methods & Applications 77, 82-93 (2013).
  20. 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).
  21. H.A. ERBAY, A. Erkip and G.M. Muslu, “The Cauchy problem for a one dimensional nonlinear elastic peridynamic model“, Journal of Differential Equations 252, 4392-4409 (2012).
  22. 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).
  23. N. Duruk, H. A. ERBAY and A. Erkip,”Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations“, Journal of Differential Equations 250, 1448-1459 (2011).
  24. G. M. Muslu and H. A. ERBAY, “Numerical simulation of blow-up solutions for the generalized Davey-Stewartson system“, International Journal of Computer Mathematics 88, 805-815 (2011).
  25. N. Duruk, H. A. ERBAY and A. Erkip,”Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity“, Nonlinearity 23, 107-118 (2010).
  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. N. Duruk, A. Erkip and H. A. ERBAY, “A higher-order Boussinesq equation in locally nonlinear theory of one-dimensional nonlocal elasticity“, IMA Journal of Applied Mathematics 74, 97-106 (2009).
  28. A. Eden, H. A. ERBAY and G. M. Muslu, “Closing the gap in the purely elliptic generalized Davey-Stewartson system“, Nonlinear Analysis: Theory, Methods & Applications 69, 2575-2581 (2008).
  29. H. Borluk, G. M. Muslu and H. A. ERBAY, “A numerical study of the long wave-short wave interaction equations“, Mathematics and Computers in Simulation 74, 113-125 (2007).
  30. A. Eden, H. A. ERBAY and G. M. Muslu, “Two remarks on a generalized Davey-Stewartson system“, Nonlinear Analysis: Theory, Methods & Applications 64, 979-986 (2006).
  31. G. M. Muslu and H. A. ERBAY, “Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation“, Mathematics and Computers in Simulation 67, 581-595 (2005).
  32. H. A. ERBAY and V. H. Tüzel, “Dynamic extension of a compressible non-linearly elastic membrane tube“, IMA Journal of Applied Mathematics 70, 25-38 (2005).
  33. J. B. Haddow and H. A. ERBAY, “A note on finite amplitude transverse waves in a thermoelastic solid“, Acta Mechanica 168, 103-110 (2004).
  34. V. H. Tüzel and H. A. ERBAY, “The dynamic response of an incompressible non-linearly elastic membrane tube sujected to a dynamic extension“, International Journal of Non-Linear Mechanics 39, 515-537 (2004).
  35. G. M. Muslu and H. A. ERBAY, “A split-step Fourier method for the complex modified Korteweg-de Vries equation“, Computers & Mathematics with Applications 45, 503-514 (2003).
  36. J.B. Haddow and H.A. ERBAY, “Some aspects of finite amplitude transverse waves in a compressible hyperelastic solid“, Quarterly Journal of Mechanics and Applied Mathematics 55, 17-28 (2002).
  37. H. A. ERBAY, Y. B. Fu and G. A. Rogerson, “Effects of pre-stress on impact waves in an incompressible elastic plate“, Quarterly Journal of Mechnics and Applied Mathematics 53, 531-550 (2000).
  38. H. A. ERBAY, “An asymptotic theory of thin micropolar plates“, International Journal of Engineering Science 38, 1497-1516 (2000).
  39. H. A. ERBAY, “Nonlinear transverse waves in a generalized elastic solid and the complex modified Korteweg-de Vries equation“, Physica Scripta 58, 9-14, (1998).
  40. H. A. ERBAY, “On the asymptotic membrane theory of thin hyperelastic plates“, International Journal of Engineering Science 35, 151-170, (1997).
  41. 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).
  42. H. A. ERBAY and H. Demiray, “Finite axisymmetric deformations of elastic tubes: An approximate method”, Journal of Engineering Mathematics 29, 451-472, (1995).
  43. S. Dost and H. A. ERBAY, “A continuum model for liquid phase electroepitaxy“, International Journal of Engineering Science 33, 1385-1402, (1995).
  44. H. A. ERBAY, “Solitary wave solutions of coupled nonlinear Schrödinger equations“, Bull. Tech. Univ. Istanbul 47, 405-413, (1994).
  45. H. A. ERBAY and S. Erbay, “Nonlinear interaction of transverse acoustical and optical waves in micropolar elastic media“, International Journal of Non-Linear Mechanics 29, 163-176, (1994).
  46. S. Erbay and H. A. ERBAY, “Nonlinear wave modulation in fluid filled distensible tubes“, Acta Mechanica 104, 201-214, (1994).
  47. 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).
  48. 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).
  49. H. A. ERBAY, S. Erbay and S. Dost, “Wave propagation in fluid-filled nonlinear viscoelastic tubes“, Acta Mechanica 95, 87-102, (1992).
  50. S. Erbay, H. A. ERBAY and S. Dost, “Nonlinear wave interactions in a micropolar elastic medium“, Wave Motion 16, 163-172, (1992).
  51. 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).
  52. 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).
  53. 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).
  54. H. A. ERBAY and E. S. Suhubi, “An asymptotic theory of thin hyperelastic plates: Part I. General Theory“, International Journal of Engineering Science 29, 447-466, (1991).
  55. H. A. ERBAY and E. S. Suhubi, “An asymptotic theory of thin hyperelastic plates: Part II. Incompressible solids and an application of the general theory“, International Journal of Engineering Science 29, 467-480, (1991).
  56. H. Demiray, H. W. Weizsacker, K. Pascale and H. A. ERBAY, “A stress-strain relation for a rat abdominal aorta“, Journal of Biomechanics 21, 369-374, (1988).
  57. 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).
  58. H. A. ERBAY, S. Erbay and H. Demiray, “Pulse waves in prestressed arteries “, Bulletin of Mathematical Biology 49, 289-305, (1987).
  59. H. Demiray and H. A. ERBAY, “An orthotropic elastic model for rat abdominal aorta“, Mathl. Modelling (Math. Comput. Model) 9, 651-658, (1987).
  60. H. A. ERBAY and H. Demiray, “Torsional vibrations of a nonlocal elastic bar“, Bull. Tech. Univ. Istanbul 38, 447-456, (1985).
  61. H. A. ERBAY and E. S. Suhubi, “A general asymptotic approximation to the nonlinear theory of thin elastic plates“, Bull. Tech. Univ. Istanbul 38, 247-272, (1985).
  62. H. A. ERBAY and H. Demiray, “Growth and decay of acceleration waves in a diatomic solid“, Bull. Tech. Univ. Istanbul 37, 331-341, (1984).