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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Two integrable third-order and fifth-order KdV equations with time-dependent coefficients: Multiple real and multiple complex soliton solutions
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Two integrable third-order and fifth-order KdV equations with time-dependent coefficients: Multiple real and multiple complex soliton solutions

机译：具有时间相关系数的两个可积分的三阶和五阶KdV方程：多个实数和多个复孤子解

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Purpose The purpose of this paper is concerned with developing two integrable Korteweg de-Vries (KdV) equations of third- and fifth-orders; each possesses time-dependent coefficients. The study shows that multiple soliton solutions exist and multiple complex soliton solutions exist for these two equations.Design/methodology/approach The integrability of each of the developed models has been confirmed by using the Painleve analysis. The author uses the complex forms of the simplified Hirota's method to obtain two fundamentally different sets of solutions, multiple real and multiple complex soliton solutions for each model.Findings The time-dependent KdV equations feature interesting results in propagation of waves and fluid flow.Research limitations/implications The paper presents a new efficient algorithm for constructing time-dependent integrable equations.Practical implications The author develops two time-dependent integrable KdV equations of third- and fifth-order. These models represent more specific data than the constant equations. The author showed that integrable equation gives real and complex soliton solutions.Social implications The work presents useful findings in the propagation of waves.Originality/value The paper presents a new efficient algorithm for constructing time-dependent integrable equations.
机译：目的本文的目的在于开发两个可分解的三阶和五阶Korteweg de-Vries（KdV）方程。每个都有与时间有关的系数。研究表明，对于这两个方程，存在多个孤子解，并且存在多个复孤子解。设计/方法/方法每种开发模型的可积性已通过Painleve分析得到证实。作者使用简化的Hirota方法的复杂形式来获得两组根本不同的解集，即每个模型的多个实数和多个复孤子解。发现与时间相关的KdV方程在波和流体传播方面具有有趣的结果。局限性/含义本文提出了一种新的构造时间相关可积方程的有效算法。实际意义作者开发了两个三阶和五阶时间相关可积KdV方程。这些模型比常数方程式代表更具体的数据。作者证明了可积方程给出了真实的和复杂的孤子解。社会意义这项工作在波的传播中提供了有用的发现。原始性/价值本文提出了一种构造依赖于时间的可积方程的新有效算法。

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