periodic solutions
(0.002 seconds)
11—20 of 28 matching pages
11: 29.3 Definitions and Basic Properties
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►For each pair of values of and there are four infinite unbounded sets of real eigenvalues for which equation (29.2.1) has even or odd solutions with periods
or .
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12: 29.8 Integral Equations
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►Let be any solution of (29.2.1) of period
, be a linearly independent solution, and denote their Wronskian.
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13: 29.19 Physical Applications
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►Simply-periodic Lamé functions ( noninteger) can be used to solve boundary-value problems for Laplace’s equation in elliptical cones.
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►Ward (1987) computes finite-gap potentials associated with the periodic Korteweg–de Vries equation.
Shail (1978) treats applications to solutions of elliptic crack and punch problems.
Hargrave (1978) studies high frequency solutions of the delta wing equation.
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14: 28.12 Definitions and Basic Properties
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►When is a rational number, but not an integer, all solutions of Mathieu’s equation are periodic with period
.
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15: 22.19 Physical Applications
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►Figure 22.19.1 shows the nature of the solutions
of (22.19.3) by graphing for both , as in Figure 22.16.1, and , where it is periodic.
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►Such solutions include standing or stationary waves, periodic cnoidal waves, and single and multi-solitons occurring in diverse physical situations such as water waves, optical pulses, quantum fluids, and electrical impulses (Hasegawa (1989), Carr et al. (2000), Kivshar and Luther-Davies (1998), and Boyd (1998, Appendix D2.2)).
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16: 29.10 Lamé Functions with Imaginary Periods
§29.10 Lamé Functions with Imaginary Periods
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29.10.3
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►are solutions of (29.2.1).
The first and the fourth functions have period
; the second and the third have period
.
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17: 28.2 Definitions and Basic Properties
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►
§28.2(vi) Eigenfunctions
…18: 1.13 Differential Equations
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