Abstract

Based on a first-order nonlinear ordinary differential equation withsix-degree nonlinear term,we first present a new auxiliary equation expansion method and itsalgorithm. Being concise and straightforward, the method isapplied to the Kundu equation. As a result, some new exacttravelling wave solutions are obtained, which include bright anddark solitary wave solutions, triangular periodic wave solutions,and singular solutions. This algorithm can also be applied toother nonlinear evolution equations in mathematical physics.

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