We consider the problem of the construction of higher terms of asymptotic many-phase soliton-type solutions of a singularly perturbed Korteweg–de Vries equation with variable coefficients and determine the accuracy with which the obtained asymptotic solution satisfies the original equation.
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V. H. Samoilenko and Yu. I. Samoilenko, “Asymptotic m-phase soliton-type solutions of a singularly perturbed Korteweg–de Vries equation with variable coefficients,” Ukr. Mat. Zh., 64, No. 7, 970–987 (2012); English translation: Ukr. Math. J., 64, No. 7, 1109–1127 (2012).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers. Definitions, Theorems, and Formulas for Reference and Review [Russian translation], Nauka, Mir (1977).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 8, pp. 1089–1105, August, 2012.
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Samoilenko, V.H., Samoilenko, Y.I. Asymptotic m-phase soliton-type solutions of a singularly perturbed Korteweg–de Vries equation with variable coefficients. II. Ukr Math J 64, 1241–1259 (2013). https://doi.org/10.1007/s11253-013-0713-x
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DOI: https://doi.org/10.1007/s11253-013-0713-x