ON THE GENERAL SOLUTIONS OF COUPLED-MODE EQUATIONS WITH VARYING COEFFICIENTS
WASHINGTON UNIV SEATTLE DEPT OF ELECTRICAL ENGINEERING
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In this report a systematic mathematical method is introduced for the solution of problems involving two coupled modes in a coupled system with varying parameters. These problems involve systems of linear differential equations with varying coefficients. By the use of a linear transformation of the dependent variables and a double diagonalization process, the coupled mode equations are reduced to two decoupled Riccati equations. The final form of the general solution is obtained in terms of four varying coupling coefficients and a transform parameter. To illustrate some applications of the method, solutions of two special cases which have been solved previously by other workers are obtained. The solutions for a number of special cases, in which the varying coefficients are specified or interrelated, are also obtained. Further possible applications are indicated.
- Numerical Mathematics
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