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2014•Advances in Difference EquationsOpen access

The general solutions of an auxiliary ordinary differential equation using complex method and its applications

Wenjun Yuan, Zifeng Huang, Maozhun Fu, Jinchun Lai

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Abstract

Abstract In this paper, we employ the complex method to obtain all meromorphic solutions of an auxiliary ordinary differential equation at first, and then find all meromorphic general solutions of in combination the Newell-Whitehead equation, the NLS equation, and the Fisher equation with degree three. Our result shows that all rational and simply periodic exact solutions of the combined the Newell-Whitehead equation, NLS equation, and Fisher equation with degree three are solitary wave solutions, and the method is simpler than other methods. MSC:30D35, 34A05.

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Abstract In this paper, we employ the complex method to obtain all meromorphic solutions of an auxiliary ordinary differential equation at first, and then find all meromorphic general solutions of in combination the Newell-Whitehead equation, the NLS equation, and the Fisher equation with degree three. Our result shows that all rational and simply periodic exact solutions of the combined the Newell-Whitehead equation, NLS equation, and Fisher equation with degree three are solitary wave solutions, and the method is simpler than other methods. MSC:30D35, 34A05.

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Available abstract

Abstract In this paper, we employ the complex method to obtain all meromorphic solutions of an auxiliary ordinary differential equation at first, and then find all meromorphic general solutions of in combination the Newell-Whitehead equation, the NLS equation, and the Fisher equation with degree three. Our result shows that all rational and simply periodic exact solutions of the combined the Newell-Whitehead equation, NLS equation, and Fisher equation with degree three are solitary wave solutions, and the method is simpler than other methods. MSC:30D35, 34A05.

Key concepts: Mathematics, Ordinary differential equation, Exact differential equation, Partial differential equation, Meromorphic function, First-order partial differential equation, Fisher's equation, Bernoulli differential equation

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