On the peakon solutions of some stochastic nonlinear evolution equations

Asif Yokus; Hatice Taskesen; Mohanad Alaloush; Betiil Deniz Demirdag

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On the peakon solutions of some stochastic nonlinear evolution equations

机译：关于一些随机非线性演化方程的高峰溶液

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摘要

In this paper, stochastic Fornberg-Whitham and a stochastic Camassa-Holm (CH) type equations are studied. A Galilean transformation which previously used for a stochastic KdV equation is employed to transform the equations into their deterministic counterparts. Then (1/G')-expansion method is used to obtain analytical solutions. 2D, 3D, and contour graphs representing the peakon solutions have been plotted by assigning special values to the constants in the solutions via computer software. In addition, by giving different random values to the external noise, the effect of the noise on the wave-forms has been exhibited. The obtained results have been discussed in detail.

机译：在本文中，研究了随机福尔格 - WHITHAM和随机CAMASSA-HOLM（CH）型方程。以前用于随机KDV方程的Galilan转换用于将方程转换为它们的确定性对应物。然后（1 / g'） - 扩展方法用于获得分析解决方案。通过计算机软件将特殊值分配给解决方案中的常数，绘制了代表峰值解决方案的2D，3D和轮廓图。另外，通过向外部噪声提供不同的随机值，已经表现出噪声对波形的影响。已经详细讨论了所得结果。

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来源
《Optical and quantum electronics》 |2021年第10期|586.1-586.17|共17页
作者
Asif Yokus; Hatice Taskesen; Mohanad Alaloush; Betiil Deniz Demirdag;
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作者单位

Department of Mathematics Firat University 23200 Elazig Turkey;

Department of Mathematics Van Yuzuncu Yil University 65080 Van Turkey;

Department of Statistics Van Yuzuncu Yil University 65080 Van Turkey;

Department of Actuary Hacettepe University 06800 Ankara Turkey;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Stochastic Camassa-Holm type equation; Stochastic Fornberg-Whitham equation; Exact solution; Noise; (1/G')-expansion;

机译：随机Camassa-Holm型方程;随机Fornberg-Whitham方程;精确的解决方案;噪音;（1 / g'） - 扩展;

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1. Stochastic functional evolution equations with monotone nonlinearity: Existence and stability of the mild solutions [J] . Jahanipur R. Journal of Differential Equations . 2010,第5期

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2. Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schrodinger and linearized stochastic Korteweg-de Vries equations [J] . Harms Philipp, Mueller Marvin S. ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees . 2019,第1期

机译：随机演化方程和应用于非线性随机波，HJMM，随机施罗德格和线性化随机Korteeg-de Vries方程的弱收敛速率
3. Dark Peakon, Kink and periodic solutions of the nonlinear Biswas-Milovic equation with Kerr law nonlinearity [J] . Akram Ghazala, Zainab Iqra Optik: Zeitschrift fur Licht- und Elektronenoptik: = Journal for Light-and Electronoptic . 2020,第期

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4. A Lyapunov criterion for mean square stability of nonlinear stochastic evolution equations [C] . Florchinger, P. . 1997

机译：非线性随机发展方程均方稳定性的Lyapunov准则
5. On uniqueness and weak convergence of solutions for the stochastic differential equations of nonlinear filtering. [D] . Lucic, Vladimir. 2001

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6. Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations [O] . Rongrong Tian, Yanbin Tang 2018

机译：随机非线性传输方程的随机熵解决方案
7. Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: the case of bounded stochastic evolutions [O] . P. L. Lions 1988

机译：完全非线性二阶方程的粘度溶液和无限尺寸中最佳随机控制。第一部分：有界随机演进的情况

On the peakon solutions of some stochastic nonlinear evolution equations

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