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A variety of novel closed-form soliton solutions to the family of Boussinesq-like equations with different types
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作者 Dipankar Kumar Gour Chandra Paul +1 位作者 Aly R.Seadawy M.T.Darvishi 《Journal of Ocean Engineering and Science》 SCIE 2022年第6期543-554,共12页
This paper deals with the closed-form solutions to the family of Boussinesq-like equations with the effect of spatio-temporal dispersion.The sine-Gordon expansion and the hyperbolic function approaches are efficiently... This paper deals with the closed-form solutions to the family of Boussinesq-like equations with the effect of spatio-temporal dispersion.The sine-Gordon expansion and the hyperbolic function approaches are efficiently applied to the family of Boussinesq-like equations to explore novel solitary,kink,anti-kink,combo,and singular-periodic wave solutions.The attained solutions are expressed by the trigonometric and hyperbolic functions including tan,sec,cot,csc,tanh,sech,coth,csch,and of their combination.In addition,the mentioned two approaches are applied to the aforesaid models in the sense of Atangana conformable derivative or Beta derivative to attain new wave solutions.Three-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying the corresponding equations of interest are provided to understand the underlying mechanisms of the stated family.For the bright wave solutions in terms of Atangana’s conformable derivative,the amplitudes of the bright wave gradually decrease,but the smoothness increases when the fractional parametersαandβincrease.On the other hand,the periodicities of periodic waves increase.The attained new wave solutions can motivate applied scientists for engineering their ideas to an optimal level and they can be used for the validation of numerical simulation results in the propagation of waves in shallow water and other nonlinear cases.The performed approaches are found to be simple and efficient enough to estimate the solutions attained in the study and can be used to solve various classes of nonlinear partial differential equations arising in mathematical physics and engineering. 展开更多
关键词 boussinesq-like equations The sine-Gordon expansion approach The hyperbolic function approach Wave solutions Atangana conformable derivative
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Solving a class of boundary value problems and fractional Boussinesq-like equation with β-derivatives by fractional-order exponential trial functions
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作者 Mohammad Parto-Haghighi Jalil Manafian 《Journal of Ocean Engineering and Science》 SCIE 2020年第3期197-204,共8页
The nonlinear two-point boundary value problem(TPBVP)is converted to a new form of the problem including integral terms.Then the combination of weak-form integral equation method(WFIEM)and special functions create a r... The nonlinear two-point boundary value problem(TPBVP)is converted to a new form of the problem including integral terms.Then the combination of weak-form integral equation method(WFIEM)and special functions create a robust and applicable numerical scheme to solve the problem.To display the accuracy of our method,some examples are investigated.Also,the fractional Boussinesq-like equation involving the β-derivative has been considered that describes the propagation of small amplitude long capillary-gravity waves on the surface of shallow water. 展开更多
关键词 Fractional order exponential trial functions BVPS Adjoint test functions Weak-form integral equation method Two-point boundary value problem Fractional boussinesq-like equation
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变系数Boussinesq型方程的Darboux变换及其精确解 被引量:1
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作者 杨苗苗 李雪梅 王涛 《河南师范大学学报(自然科学版)》 CAS CSCD 北大核心 2011年第3期13-15,共3页
变系数Boussinesq型方程在某种约束下与变系数Broer-Kaup-Kupershmidt方程之间的关系,通过构造变系数Broer-Kaup-Kupershmidt方程的Darboux变换并应用Darboux变换得到变系数Boussinesq型方程的孤子解.
关键词 变系数Boussinesq型方程 DARBOUX变换 孤子解
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分数阶变分迭代法处理分数阶类Boussinesq方程(英文)
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作者 顾佳磊 夏铁成 《应用数学与计算数学学报》 2011年第1期46-52,共7页
分数阶变分迭代法(FVIM)是一种处理分数阶微分方程的有效工具.用分数阶变分迭代法求解了时间分数阶类Boussinesq方程,并且作为一种特殊情况,得到了类Boussinesq方程B(2.2)的单孤子解.
关键词 修正的Riemann-Liouville导数 分数阶变分迭代法 类Boussinesq方程
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(3+1)维Boussinesq方程的新精确解 被引量:1
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作者 时迎柱 戴正德 +1 位作者 周秀环 宋爱菊 《广西工学院学报》 CAS 2009年第3期56-59,共4页
为了获得(3+1)维Boussinesq方程新的精确解,采用齐次平衡方法,通过使用数学计算软件Maple给出了Riccati辅助方程的不同形式的新解,从而解得了(3+1)维Boussinesq方程的一些类周期波解和类孤立波解.这些新的精确解丰富了Boussinesq方程解... 为了获得(3+1)维Boussinesq方程新的精确解,采用齐次平衡方法,通过使用数学计算软件Maple给出了Riccati辅助方程的不同形式的新解,从而解得了(3+1)维Boussinesq方程的一些类周期波解和类孤立波解.这些新的精确解丰富了Boussinesq方程解的理论. 展开更多
关键词 (3+1)维Boussinesq方程 齐次平衡方法 Riccati辅助方程 类周期波解 类孤立波解
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Boussinesq方程的精确孤子解研究
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作者 史曙光 刘东生 《阜阳师范学院学报(自然科学版)》 2018年第4期1-4,21,共5页
本文通过Jumarie的改性Riemann Liouville导数构建时间分数阶Boussinesq方程;应用函数变量法得到了这些时间分数阶方程的精确孤子解,这些精确解可以描述周期波和孤立波;导出的解在海洋工程中有许多潜在的应用,结果表明函数变量法求解分... 本文通过Jumarie的改性Riemann Liouville导数构建时间分数阶Boussinesq方程;应用函数变量法得到了这些时间分数阶方程的精确孤子解,这些精确解可以描述周期波和孤立波;导出的解在海洋工程中有许多潜在的应用,结果表明函数变量法求解分数阶微分方程简单有效。 展开更多
关键词 孤子解 精确解 时间分数阶Boussinesq方程 函数变量法
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一类变系数Boussinesq型方程的Darboux变换及多孤子解
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作者 杨苗苗 王涛 李雪梅 《数学的实践与认识》 北大核心 2018年第8期206-211,共6页
主要讨论在某种约束下,变系数Boussinesq型方程和变系数Broer-KaupKupershmidt方程之间的联系,构造变系数Broer-Kaup-Kupershmidt方程的另外一种Darboux变换,且应用Darboux变换得到变系数Boussinesq型方程的孤子解.
关键词 变系数Boussinesq型方程 变系数Broer-Kaup-Kupershmidt方程 DARBOUX变换 孤子解
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一类变系数Boussinesq型方程的精确解
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作者 杨苗苗 蒋雯丽 《数学的实践与认识》 北大核心 2019年第6期305-310,共6页
一类变系数Boussinesq型方程与变系数Broer-Kaup-Kupershmidt方程之间在某种约束下的关系.通过构造变系数Broer-Kaup-Kupershmidt方程的达布变换并应用达布变换得到这类变系数Boussinesq型方程的精确解.
关键词 变系数Boussinesq型方程 变系数Broer-Kaup-Kupershmidt方程 达布变换 精确解
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