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The generalization of modal subspaces in the complex domain

Published online by Cambridge University Press:  24 October 2008

H. Swann ,
C. P. Atkinson  and
B. L. Dhoopar
H. Swann
Affiliation:
University of California, Berkeley, and Indian Institute of Technology, Kanpur, India
C. P. Atkinson
Affiliation:
University of California, Berkeley, and Indian Institute of Technology, Kanpur, India
B. L. Dhoopar
Affiliation:
University of California, Berkeley, and Indian Institute of Technology, Kanpur, India
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Extract

The purpose of this paper is to present the concept of ‘modal subspaces’ for systems of coupled non-linear autonomous homogeneous second-order differential equations of the complex variables z1, z2. This development is an extension of the previous paper, entitled ‘Modal subspaces in the complex domain’, by Atkinson and Swann (6), which dealt with a pair of coupled non-linear autonomous homogeneous second-order differential equations of the form

Differentiation is with respect to a real variable t and ajk and bjk are constants which may be complex: n is any positive integer: f1 and f2 are the real and imaginary parts respectively of g1 and g2 are real and imaginary parts respectively of and zj = xj + iyj (j = 1, 2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 731 - 740
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

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