Geodesic
Solution of Chew–Low equations in the quadratic approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 3, pp. 384-392 
V. P. Gerdt; A. Yu. Zharkov. Solution of Chew–Low equations in the quadratic approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 3, pp. 384-392. http://geodesic.mathdoc.fr/item/TMF_1982_52_3_a4/
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     title = {Solution of {Chew{\textendash}Low} equations in the quadratic approximation},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_52_3_a4/}
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The second-order power contributions are found in the framework of the iterative scheme of construction of the general Chew–Low equation [1] proposed by Gerdt [2]. In contrast to the linear approximation obtained by Gerdt, the quadratic approximation has an infinite number of poles in the complex plane of the uniformizing variable $w$. It is shown that allowance for the quadratic corrections in the general solution makes it possible to distinguish the class of solutions possessing the required Born pole at the point $w=0$. The most cumbersome part of the analytic computations in the present study was done on a computer using the algebraic system REDUCE-2.

[1] Chew G. F., Low F. E., Phys. Rev., 101:5 (1956), 1570–1579 | DOI | MR | Zbl

[2] Gerdt V. P., O globalnoi strukture obschego resheniya uravnenii Chu-Lou, Preprint R2-80-436, OIYaI, Dubna, 1980

[3] Zhuravlev V. I., Mescheryakov V. A., EChAYa, 5:1 (1974), 172–222 | MR

[4] Gerdt V. P., Mescheryakov V. A., TMF, 24:2 (1975), 155–163 | MR

[5] Gerdt V. P., Lokalnoe postroenie obschego resheniya uravnenii Chu-Lou s pomoschyu EVM. Trudy Mezhdunarodnogo soveschaniya po sistemam i metodam analiticheskikh vychislenii na EVM i ikh primeneniyu v teoreticheskoi fizike, D11-80-13, OIYaI, Dubna, 1980, 159–169

[6] Hearn A. S., REDUCE User's Manual, Second Edition, Univ of Utah, 1973

[7] Gerdt V. P., Tarasov O. V., Shirkov D. V., UFN, 130:1 (1980), 113–147 | DOI | MR

[8] Mescheryakov V. A., Rerikh K. V., TMF, 3:1 (1970), 78–93 | MR

[9] Mescheryakov V. A., Invariantnye mnogoobraziya uravneniya Chu-Lou, Preprint R2-5906, OIYaI, Dubna, 1971

[10] Gerdt V. P., ZhVM i MF, 19:6 (1979), 1601–1608 | MR

[11] Rerikh K. V., Uravneniya Chu-Lou kak preobrazovaniya Kremona. Struktura obschikh integralov, Preprint R2-80728, OIYaI, Dubna, 1980

[12] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, t. 1, Nauka, M., 1973 | MR

[13] Gerdt V. P., Zhuravlev V. I., Mescheryakov V. A., YaF, 20:4 (1974), 756–761