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The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

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Abstract

In this paper, the famous Klein–Gordon–Zakharov (KGZ) equations are first generalized, and the new special types of KGZ equations with the positive fractional power terms (gKGZE) are presented. In order to derive exact solutions of the new special gKGZE, subsidiary higher-order ordinary differential equations (sub-ODEs) with the positive fractional power terms are introduced, and with the aid of the sub-ODE, exact solutions of four special types of the gKGZE are derived, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal travelling wave solution, provided that the coefficients of gKGZE satisfy certain constraint conditions.

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Acknowledgement

The authors would like to express their sincere thanks to the referees for their valuable suggestions.This project is supported in part by the Basic Science and the Front Technology Research Foundation of Henan Province of China (Grant No. 092300410179) and the Scientific Research Innovation Ability Cultivation Foundation of Henan University of Science and Technology (Grant No. 011CX011).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, China

    JINLIANG ZHANG, WUQIANG HU & YU MA

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  1. JINLIANG ZHANG
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  2. WUQIANG HU
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  3. YU MA
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Correspondence to JINLIANG ZHANG.

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ZHANG, J., HU, W. & MA, Y. The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions. Pramana - J Phys 87, 93 (2016). https://doi.org/10.1007/s12043-016-1293-8

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  • DOI: https://doi.org/10.1007/s12043-016-1293-8

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