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Korteweg–de Vries (KdV)-typed equations are seen in fluid dynamics, plasma physics and other fields. By means of the Bell-polynomial procedure, we take two higher-order members of the KdV hierarchy, the seventh- and ninth-order Lax’s KdV equations in fluid dynamics, as the examples for studying the integrable properties of the higher-order equations. Different from lower-order equations, two new partial...
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