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Teoreticheskaya i Matematicheskaya Fizika, 1983, Volume 55, Number 3, Pages 469–474
(Mi tmf2183)
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Cubic approximation and local restrictions on the functional arbitrariness in the general solution of the Chew–Low equations
V. P. Gerdt, A. Yu. Zharkov
Abstract:
The power-law expansion of the general solution of the Chew–Low equations [3]
proposed by the authors [1, 2] is considered in the neighborhood of the point $w=0$. It is shown that, in contrast to the quadratic approximation, the cubic approximation does not have the required Born pole at this point. It is concluded from this that the expansion is not valid near the Born pole. In the class of physically interesting solutions, the local restrictions $\beta(0)=0$ and $C(0)\ne0$ are obtained for the arbitrary periodic functions $\beta(w)$ and $C(w)$ that determine the general solution. By numerical analysis, the value $C(0)\approx-265$ is obtained for solutions with Born pole.
Received: 10.10.1982
Citation:
V. P. Gerdt, A. Yu. Zharkov, “Cubic approximation and local restrictions on the functional arbitrariness in the general solution of the Chew–Low equations”, TMF, 55:3 (1983), 469–474; Theoret. and Math. Phys., 55:3 (1983), 626–629
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https://www.mathnet.ru/eng/tmf2183 https://www.mathnet.ru/eng/tmf/v55/i3/p469
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Abstract page: | 237 | Full-text PDF : | 69 | References: | 43 | First page: | 1 |
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