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Abstract
It is well known that different types of exact solutions of an auxiliary equation produce new types of exact travelling wave solutions to nonlinear equations. In this paper, by means of symbolic computation, the new solutions of original auxiliary equation of first-order nonlinear ordinary differential equation with a sixth-degree nonlinear term are presented to obtain novel exact solutions of the Kawahara equation. By the aid of the solutions of the original auxiliary equation, some other physically important nonlinear equations can be solved to construct novel exact solutions.
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