References
- W.F. Ames, S.Y. Lee and A.A. Vicario. Longitudinal wave propagation on a traveling threadline–II. International Journal of Non-Linear Mechanics, 5(3):413–426, 1970. https://doi.org/10.1016/0020-7462(70)90004-1.
- W.F. Ames and A.A. Vicario. On the longitudinal wave propagation on a traveling threadline. Dev. Mech., 3(5):733–746, 1969.
- R. Arora. Asymptotical solutions for a vibrationally relaxing gas. Mathematical Modelling and Analysis, 14(4):423–434, 2009. https://doi.org/10.3846/1392- 6292.2009.14.423-434.
- G.K. Batchelor. An Introduction to Fluid Dynamics. Cambridge Mathematical Library. Cambridge University Press, 1967. https://doi.org/10.1017/CBO9780511800955.
- G.F. Carrier. On the non-linear vibration problem of the elastic string. Quarterly of applied mathematics, 3:157–165, 1945. https://doi.org/10.1090/qam/12351.
- G.F. Carrier. A note on the vibrating string. Quarterly of applied mathematics, 7:97–101, 1949. https://doi.org/10.1090/qam/28511.
- L.-Q. Chen. Analysis and control of transverse vibrations of axially moving strings. Applied Mechanics Reviews, 58(2):91–116, 2005. https://doi.org/10.1115/1.1849169.
- L.-Q. Chen and H. Ding. Two nonlinear models of a transversely vibrating string. Archive of Applied Mechanics, 78(5):321–328, 2008. https://doi.org/10.1007/s00419-007-0164-7.
- E.V. Ferapontov and K.R. Khusnutdinova. The Haantjes tensor and double waves for multi-dimensional systems of hydrodynamic type: a necessary condition for integrability. Proceedings of the Royal Society A, 462:1197–1219, 2006. https://doi.org/10.1098/rspa.2005.1627.
- E.V. Ferapontov and D.G. Marshall. Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor. Mathematische Annalen, 339(1):61–99, 2007. https://doi.org/10.1007/s00208-007-0106-2.
- E.R. Gutierrez, P.L. Silva Dias and C. Raupp. Asymptotic approach for the nonlinear equatorial long wave interactions. Journal of Physics: Conference Series, 285(1):012020, 2011.
- V.V. Kozlov and S.D. Furta. Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations. Springer Monographs in Mathematics. SpringerVerlag, Berlin, Heidelberg, 2013.
- A. Krylovas. Justification of the method of internal averaging along characteristics of weakly linear systems. I. Lithuanian Mathematical Journal, 29(4):721–732, 1989.
- A. Krylovas. Justification of the method of internal averaging along characteristics of weakly nonlinear systems. II. Lithuanian Mathematical Journal, 30(1):35–43, 1990. https://doi.org/10.1007/BF00966457.
- A. Krylovas and R. Čiegis. Asymptotic approximation of hyperbolic weakly nonlinear system. Journal Nonlinear Mathematical Physics, 8(4):458–470, 2001. https://doi.org/10.2991/jnmp.2001.8.4.2.
- A. Krylovas and R. Čiegis. A review of numerical asymptotic averaging for weakly nonlinear hyperbolic waves. Mathematical Modelling and Analysis, 9(3):209–222, 2004. https://doi.org/10.1080/13926292.2004.9637254.
- A. Krylovas, O. Lavcel-Budko and P. Miškinis. Asymptotic solution of the mathematical model of nonlinear oscillations of absolutely elastic inextensible weightless string. Nonlinear Analysis: Modelling and Control, 15(3):307–323, 2010.
- A. Krylovas and P. Miškinis. Nonlinear oscillations of the absolute elastic weightless string. Asymptotics construction. Lithuanian Mathematical Journal, spec. issue, 47:123–127, 2007.
- A. Krylovas and P. Miškinis. Properties of averaging along the characteristics hyperbolic of the system operator. Lithuanian Mathematical Journal, spec. issue, 53(B):25–30, 2012.
- E. Kurihara and T. Yano. Nonlinear analysis of periodic modulation in resonances of cylindrical and spherical acoustic standing waves. Physics of Fluids, 18(11):117107, 2006. https://doi.org/10.1063/1.2393437.
- A.W. Leissa and A.M. Saad. Large amplitude vibrations of strings. Journal of Applied Mechanics, 61(2):296–301, 1994. https://doi.org/10.1115/1.2901444.
- P. Miškinis. Nonlinear and nonlocal integrable models (in Lithuanian). Technika, Vilnius, Lithuania, 2003.
- Y.A. Mitropolsky and Nguen Van Dao. Applied Asymptotic Methods in Nonlinear Oscillations. Solid Mechanics and Its Applications. Springer, Netherlands, 1997. https://doi.org/10.1007/978-94-015-8847-8.
- Y.A. Mitropolsky, G. Khoma and M. Gromyak. Asymptotic Methods for investigating Quasiwave Equations of Hyperbolic Type. Kluwer Academic Publishers, Dordrecht, 2006.
- A.S. Vasudeva Murthy. On the string equation of Narasimha. In Rajendra (ed.) et al. Bhatia (Ed.), Connected at infinity II. A selection of mathematics by Indians, pp. 58–84, New Delhi, 2012. Hindustan Book Agency. Texts and Readings in Mathematics 67.
- A. Nayfeh. Introduction to Perturbation Technigues. John Wiley & Sons, Inc., New York, Chichester, Brisbabe, Toronto, 1981.
- D.E. Pelinovsky, G. Simpson and M.I. Weinstein. Polychromatic solytary waves in a periodic and nonlinear Maxwell system. SIAM Journal on Applied Dynamical Systems, 11(1):478–506, 2012. https://doi.org/10.1137/110837899.
- V.D. Sharma and G.K. Srinivasan. Wave interaction in a nonequilibrium gas flow. International Journal of Non-Linear Mechanics, 40(7):1031–1040, 2005. https://doi.org/10.1016/j.ijnonlinmec.2005.02.003.
- G. Simpson and M.I. Weinstein. Coherent structures and carries shocks in the nonlinear periodic Maxwell equation. Multiscale Modeling & Simulation, 9(3):955–990, 2011. https://doi.org/10.1137/100810046.
- W.A. Strauss. Partial Differential Equations. An Introduction. Jon Wiley & Sons, Ltd., 2008.
- T. Witelski and M. Bowen. Methods of Mathematical Modelling. Continuous Systems and Differential Equations. Springer Undergraduate Mathematics Series. Springer International Publishing, Switzerland, 2015. https://doi.org/10.1007/978-3-319-23042-9.