Roshid Md Mamunur, Roshid Harun-Or
Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh.
Heliyon. 2018 Aug 31;4(8):e00756. doi: 10.1016/j.heliyon.2018.e00756. eCollection 2018 Aug.
Two nonlinear evolution equations, namely the Kadomtsev-Petviashvili (KP) equation which describes the dynamics of soliton and nonlinear wave in the field of fluid dynamics, plasma physics and the Oskolkov equation which describes the dynamics of an incompressible visco-elastic Kelvin-Voigt fluid are investigated. We deliberate exact traveling wave solutions, specially kink wave, cusp wave, periodic breather waves and periodic wave solutions of the models applying the modified simple equation method. The solutions can be expressed explicitly. The dynamics of obtained wave solutions are analyzed and illustrated in figures by selecting appropriate parameters. The modified simple equation method is reliable treatment for searching essential nonlinear waves that enrich variety of dynamic models arises in engineering fields.
研究了两个非线性演化方程，即描述流体动力学、等离子体物理学领域中孤子和非线性波动力学的Kadomtsev-Petviashvili（KP）方程，以及描述不可压缩粘弹性开尔文-沃伊特流体动力学的奥斯科尔科夫方程。我们运用改进的简单方程法来求解这些模型的精确行波解，特别是扭结波、尖点波、周期呼吸波和周期波解。这些解可以明确地表示出来。通过选择合适的参数，对所得到的波解的动力学进行了分析并在图中进行了说明。改进的简单方程法是寻找基本非线性波的可靠方法，丰富了工程领域中出现的各种动力学模型。
