W. A. Strauss's research while affiliated with Brown University and other places

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Publications (1)

Nonlinear Scattering Theory
  • Article

January 1974

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25 Reads

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143 Citations

W. A. Strauss

Scattering theory compares the behavior in the distant future and past of a system evolving in time. It is called nonlinear if the system evolves in a nonlinear fashion. Consider a one-parameter group of operators on some linear space X: $$ U(t)U(s) = U(t + s);U(o) = I $$ -∞ <t, s <+∞. We think of U(t)f as representing the state at time t beginning with a state f ε X at time zero. We are interested in the behavior of U(t)f as t → ±∞ and in the relationship between the behavior at +∞ and at −∞.

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Citations (1)

... Formula (1.4) is a kind of the small amplitude limit. In the study of inverse scattering problems for nonlinear dispersive equations, the small amplitude limit is the most essential tool (see, e.g., [15,19,21,25,26,30,34]). In the case of N ≥ 5, unfortunately, we can not expect that (1.5) holds true because of the term O(λ 5 ) in (1.4). ...

Reference:

On inverse scattering for the two-dimensional nonlinear Klein-Gordon equation
Nonlinear Scattering Theory
  • Citing Article

  • January 1974

W. A. Strauss