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Lump Solutions and Interaction Solutions for the Dimensionally Reduced Nonlinear Evolution Equation

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  • Baoyong Guo
  • Huanhe Dong
  • Yong Fang

Abstract

In this paper, by means of the Hirota bilinear method, a dimensionally reduced nonlinear evolution equation is investigated. Through its bilinear form, lump solutions are obtained. We construct interaction solutions between lump solutions and one soliton solution by choosing quadratic functions and exponential function. Interaction solutions with the combinations of exponential functions and sine function are also given. Meanwhile, the figures of these solutions are plotted. The dynamical characteristics and properties of obtained solutions are discussed, respectively. The results show that the corresponding physical quantities and properties of nonlinear waves are associated with the values of the parameters.

Suggested Citation

  • Baoyong Guo & Huanhe Dong & Yong Fang, 2019. "Lump Solutions and Interaction Solutions for the Dimensionally Reduced Nonlinear Evolution Equation," Complexity, Hindawi, vol. 2019, pages 1-9, October.
    • Handle: RePEc:hin:complx:5765061
    DOI: 10.1155/2019/5765061
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    References listed on IDEAS

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    1. Russo, Matthew & Choudhury, S. Roy, 2017. "Analytic solutions of a microstructure PDE and the KdV and Kadomtsev–Petviashvili equations by invariant Painlevé analysis and generalized Hirota techniques," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 228-239.
    2. Wen-Xiu Ma & Jie Li & Chaudry Masood Khalique, 2018. "A Study on Lump Solutions to a Generalized Hirota-Satsuma-Ito Equation in (2+1)-Dimensions," Complexity, Hindawi, vol. 2018, pages 1-7, December.
    3. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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