Publications

Journal Articles

  1. H.A. ERBAY, S. Erbay and A. Erkip, “Convergence of a semi-discrete  numerical method for a class of nonlocal nonlinear wave equations” (submitted).
  2. H.A. ERBAY, S. Erbay and A. Erkip, “Comparison of nonlocal nonlinear wave equations in the long-wave limit” (submitted).
  3. 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).
  4. 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).
  5. 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).
  6. 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).
  7.  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).
  8. 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).
  9. 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).
  10. H.A. ERBAY, S. Erbay and A. Erkip, “Derivation of the Camassa-Holm equations for elastic waves“, Physics Letters A  379, 956-961 (2015).
  11. 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).
  12. 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).
  13. 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).
  14. 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).
  15. 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).
  16. 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).
  17. 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).
  18. 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).
  19. 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).
  20. 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).
  21. 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).
  22. 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).
  23. 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).
  24. 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).
  25. 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).
  26. 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).
  27. J. B. Haddow and H. A. ERBAY, “A note on finite amplitude transverse waves in a thermoelastic solid“, Acta Mechanica 168, 103-110 (2004).
  28. 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).
  29. 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).
  30. 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).
  31. 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).
  32. H. A. ERBAY, “An asymptotic theory of thin micropolar plates“, International Journal of Engineering Science 38, 1497-1516 (2000).
  33. 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).
  34. H. A. ERBAY, “On the asymptotic membrane theory of thin hyperelastic plates“, International Journal of Engineering Science 35, 151-170, (1997).
  35. 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).
  36. H. A. ERBAY and H. Demiray, “Finite axisymmetric deformations of elastic tubes: An approximate method”, Journal of Engineering Mathematics 29, 451-472, (1995).
  37. S. Dost and H. A. ERBAY, “A continuum model for liquid phase electroepitaxy“, International Journal of Engineering Science 33, 1385-1402, (1995).
  38. H. A. ERBAY, “Solitary wave solutions of coupled nonlinear Schrödinger equations“, Bull. Tech. Univ. Istanbul 47, 405-413, (1994).
  39. 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).
  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. 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).
  49. 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).
  50. 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).
  51. 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).
  52. H. A. ERBAY, S. Erbay and H. Demiray, “Pulse waves in prestressed arteries “, Bulletin of Mathematical Biology 49, 289-305, (1987).
  53. H. Demiray and H. A. ERBAY, “An orthotropic elastic model for rat abdominal aorta“, Mathl. Modelling (Math. Comput. Model) 9, 651-658, (1987).
  54. H. A. ERBAY and H. Demiray, “Torsional vibrations of a nonlocal elastic bar“, Bull. Tech. Univ. Istanbul 38, 447-456, (1985).
  55. 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).
  56. H. A. ERBAY and H. Demiray, “Growth and decay of acceleration waves in a diatomic solid“, Bull. Tech. Univ. Istanbul 37, 331-341, (1984).