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Analytical solution of wave system in R~n with coupling controllers

机译：耦合控制器在R〜n中波动系统的解析解

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Purpose - The purpose of this paper is to consider analytical solution of wave system in R~n with coupling controllers by using the homotopy perturbation method (HPM). Design/methodology/approach - HPM is applied to the system of linear partial differential equations, i.e. the system of waves in the two-dimensional version of system equations (1) and (2). This problem is motivated by an analogous problem in ordinary differential equations for coupled oscillators and has potential application in isolating a vibrating object from the outside disturbances. For example, rubber or rubber-like materials can be used to either absorb or shield a structure from vibration. As an approximation, these materials can be modeled as distributed springs. Findings - In this paper, HPM was used to obtain analytical solution of wave system in with coupling controllers. The method provides the solutions in the form of a series with easily computable terms. Unlike other common methods for solving any physical problem, linear or nonlinear, that requires linearization, discretization, perturbation, or unjustified assumptions that may slightly change the physics of the problem, the HPM finds approximate analytical solutions by using the initial conditions only. Originality/value - The method proposed in this paper is very reliable and efficient and is being used quite extensively for diversified nonlinear problems of a physical nature. The algorithm is being used for the first time on such problems.
机译：目的-本文的目的是通过同伦摄动法（HPM）考虑带有耦合控制器的R〜n中波动系统的解析解。设计/方法/方法-HPM适用于线性偏微分方程组，即系统方程（1）和（2）的二维版本中的波浪系统。这个问题是由耦合振荡器的常微分方程中的一个类似问题引起的，并且在将振动物体与外界干扰隔离方面具有潜在的应用。例如，橡胶或类橡胶材料可用于吸收或屏蔽结构免受振动。作为近似，可以将这些材料建模为分布式弹簧。发现-本文将HPM用于带有耦合控制器的波动系统的解析解。该方法以具有容易计算的项的系列的形式提供解决方案。与其他解决线性或非线性物理问题的常用方法不同，线性或非线性需要线性化，离散化，微扰或不合理的假设，这些假设可能会稍微改变问题的物理性质，因此HPM仅通过使用初始条件即可找到近似的解析解。原创性/价值-本文提出的方法非常可靠和有效，并且已广泛用于解决各种物理性质的非线性问题。该算法首次用于此类问题。

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