Abstract
In this section we consider a simple application of the results of Section 6.1 to the initial value problem for the following nonlinear Schrödinger equation in ∝2
where u is a complex valued function and k a real constant. The space in which this problem will be considered is L2(R2). Defining the linear operator A 0 by D(A 0 ) = H2(R2)and A 0 u = — i & u for u ϵ D(A0) the initial value problem (1.1) can be rewritten as
where F(u) = ik\u\2u.
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© 1983 Springer-Verlag New York, Inc.
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Pazy, A. (1983). Applications to Partial Differential Equations—Nonlinear Equations. In: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, vol 44. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5561-1_8
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DOI: https://doi.org/10.1007/978-1-4612-5561-1_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5563-5
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