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Inverse Scattering Method

  • Richard H. Enns
  • George C. McGuire
Chapter

Abstract

The inverse scattering method (ISM) is important because it allows the use of linear techniques to solve the initial value problem for a wide variety of nonlinear wave equations of physical interest and to obtain N-soliton (N = 1, 2, 3,…) solutions. The KdV two-soliton solution was the subject of Maple file 8 where it was animated. The ISM was first discovered and developed by Gardner, Greene, Kruskal and Miura [GGKM67] for the KdV equation. A general formulation of the method by Peter Lax [Lax68] soon followed. This nontrivial formulation is the subject of the next few sections. It is presented to give the reader the flavor of a more advanced topic in nonlinear physics. As you will see, the inverse scattering method derives its name from its close mathematical connection for the KdV case to the quantum mechanical scattering of a particle by a localized potential or tunnelling through a barrier.

Keywords

Transmission Coefficient Direct Problem Input Shape Inverse Scattering Method Inverse Scatter Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Richard H. Enns
    • 1
  • George C. McGuire
    • 2
  1. 1.Department of PhysicsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of PhysicsUniversity College of the Fraser ValleyAbbotsfordCanada

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