Linear and Nonlinear Physical Models

  • Abdul-Majid Wazwaz
Part of the Nonlinear Physical Science book series (NPS)


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.


Recursive Relation Burger Equation Variational Iteration Schrodinger Equation Variational Iteration Method 
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  1. 1.
    M.J. Ablowitz and P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, (1991).zbMATHCrossRefGoogle Scholar
  2. 2.
    M.J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981).zbMATHGoogle Scholar
  3. 3.
    G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, (1994).zbMATHGoogle Scholar
  4. 4.
    J.M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech. 1, 171–199, (1948).CrossRefMathSciNetGoogle Scholar
  5. 5.
    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).zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    J.H. He, Some asymptotic methods for strongly nonlinearly equations, Int. J. of Modern Math., 20(10), 1141–1199, (2006).zbMATHGoogle Scholar
  7. 7.
    W. Gereman and A. Nuseir, Symbolic methods to construct exact solutions of nonlinear partial differential equations, Math. Comput. Simulation, 43, 13–27, (1997).CrossRefMathSciNetGoogle Scholar
  8. 8.
    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).zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, (2004).zbMATHCrossRefGoogle Scholar
  10. 19.
    R. Hirota, Exact solutions of the Sine-Gordon equation for multiple collisions of solitons, J. Phys. Soc. Japan, 33(5), 1459–1463, (1972).CrossRefGoogle Scholar
  11. 11.
    R.M. Miura, The Korteweg de-Vries equation: a survey of results, SIAM Rev., 18, 412–459, (1976).zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    A.M. Wazwaz, The decomposition method for approximate solution of the Goursat problem, Appl. Math. Comput, 69, 299–311, (1995).zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    A.M. Wazwaz, A new approach to the nonlinear advection problem, an application of the decomposition method, Appl. Math. Comput., 72, 175–181, (1995).zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    A.M. Wazwaz, Necessary conditions for the appearance of noise terms in decomposition solution series, Appl. Math. Comput., 81, 199–204, (1997).CrossRefMathSciNetGoogle Scholar
  15. 15.
    A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Leiden, (2002).zbMATHGoogle Scholar
  16. 16.
    G.B. Whitham, Linear and Nonlinear Waves, John Wiley, New York, (1976).Google Scholar

Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Abdul-Majid Wazwaz
    • 1
  1. 1.Department of MathematicsSaint Xavier UniversityChicagoUSA

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