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Periodic solutions for Hamiltonian equation associated with Gaussian potential

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Abstract

This paper is focused on the approximate procedures for the periodic solutions of the nonlinear Hamilton equation with Gaussian potential. We propose a modified rational harmonic balance method to treat conservative nonlinear equations without the requirements on small perturbation or small parameter. The different approximating orders of this scheme illustrate the excellent agreement of the approximate frequencies with the exact ones. All the numerical results reveal that this effective method can be widely applied to many other truly nonlinear differential equations.

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Acknowledgments

We wish to thank the referee for his/her careful reading of the manuscript and for valuable comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Georgetown University, Washington D.C., 20057, USA

    Der-Chen Chang

  2. Department of Mathematics, Fu Jen Catholic University, Taipei, 242, Taiwan, ROC

    Der-Chen Chang

  3. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, People’s Republic of China

    Sheng-Ya Feng

  4. School of Mathematical Sciences and Key Lab of Mathematics for Nonlinear Science, Fudan University, Shanghai, 200433, People’s Republic of China

    Sheng-Ya Feng

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  1. Der-Chen Chang
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Correspondence to Sheng-Ya Feng.

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Funding

The first author is partially supported by an NSF grant DMS-1408839 and a McDevitt Endowment Fund at Georgetown University. The second author is partially supported by the National Natural Science Foundation of China (Grant No. 11426109 and No. 11501203), as well as the Fundamental Research Funds for the Central Universities of China (Grant No. 22A201514035).

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Chang, DC., Feng, SY. Periodic solutions for Hamiltonian equation associated with Gaussian potential. Anal.Math.Phys. 7, 459–477 (2017). https://doi.org/10.1007/s13324-016-0149-1

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  • DOI: https://doi.org/10.1007/s13324-016-0149-1

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