Journal article
A solution of an operator equation related to the KdV equation
Linear algebra and its applications, v 418(2), pp 788-792
15 Oct 2006
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Abstract
For a given nonzero bounded linear operator
A on a Banach space
X, we show that if
A or
A
∗ has an eigenvalue then, except when the dimension of
X is equal to two and the trace of
A is zero, there exists a bounded linear operator
B on
X such that (i)
AB
+
BA is of rank one, and (ii)
I
+
f(
A)
B is invertible for every function
f analytic in a neighborhood of the spectrum of
A. This result was motivated by the operator method used by Carl et al. [H. Aden, B. Carl, On realizations of solutions of the KdV equation by determinants on operator ideals, J. Math. Phys. 37 (1996) 1833–1857; H. Blohm, Solution of nonlinear equations by trace methods, Nonlinearity 13 (2000) 1925–1964; B. Carl, C. Schiebold, Nonlinear equations in soliton physics and operator ideals, Nonlinearity 12 (1999) 333–364; B. Carl, S.-Z. Huang, On realizations of solutions of the KdV equation by the
C
0-semigroup method, Amer. J. Math. 122 (2000) 403–438; S.-Z. Huang, An operator method for finding exact solutions to vector Korteweg–de Vries equations, J. Math. Phys. 44 (2003) 1357–1388] to solve nonlinear partial differential equations such as the Korteweg–deVries (KdV), modified KdV, and Kadomtsev–Petviashvili equations.
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Details
- Title
- A solution of an operator equation related to the KdV equation
- Creators
- Ramesh V. Garimella - University of Central ArkansasVolodymyr Hrynkiv - University of Tennessee at KnoxvilleA.R. Sourour - University of Victoria
- Publication Details
- Linear algebra and its applications, v 418(2), pp 788-792
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000241258500031
- Scopus ID
- 2-s2.0-33748147806
- Other Identifier
- 991021861630104721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied