Abstract
This chapter is devoted to treatments of linear and nonlinear particular applications that appear in applied sciences. A wide variety of physically significant problems modeled by linear and nonlinear partial differential equations has been the focus of extensive studies for the last decades. A huge size of research and investigation has been invested in these scientific applications. Several approaches have been used such as the characteristics method, spectral methods and perturbation techniques to examine these problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.J. Ablowitz and P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, (1991).
M.J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981).
G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, (1994).
J.M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech. 1, 171–199, (1948).
D.J. Evans and B.B. Sanugi, Numerical solution of the Goursat problem by a nonlinear trapezoidal formula, Appl. Math. Lett., 1(3), 221–223, (1988).
J.H. He, Some asymptotic methods for strongly nonlinearly equations, Int. J. of Modern Math., 20(10), 1141–1199, (2006).
W. Gereman and A. Nuseir, Symbolic methods to construct exact solutions of nonlinear partial differential equations, Math. Comput. Simulation, 43, 13–27, (1997).
J. Hietarinta, A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations, J. Math. Phys., 28(8), 1732–1742, (1987).
R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, (2004).
R. Hirota, Exact solutions of the Sine-Gordon equation for multiple collisions of solitons, J. Phys. Soc. Japan, 33(5), 1459–1463, (1972).
R.M. Miura, The Korteweg de-Vries equation: a survey of results, SIAM Rev., 18, 412–459, (1976).
A.M. Wazwaz, The decomposition method for approximate solution of the Goursat problem, Appl. Math. Comput, 69, 299–311, (1995).
A.M. Wazwaz, A new approach to the nonlinear advection problem, an application of the decomposition method, Appl. Math. Comput., 72, 175–181, (1995).
A.M. Wazwaz, Necessary conditions for the appearance of noise terms in decomposition solution series, Appl. Math. Comput., 81, 199–204, (1997).
A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Leiden, (2002).
G.B. Whitham, Linear and Nonlinear Waves, John Wiley, New York, (1976).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2009 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wazwaz, AM. (2009). Linear and Nonlinear Physical Models. In: Partial Differential Equations and Solitary Waves Theory. Nonlinear Physical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00251-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-00251-9_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00250-2
Online ISBN: 978-3-642-00251-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)