Lie symmetry analysis, conservation laws and solitary wave solutions to a fourth-order nonlinear generalized Boussinesq water wave equation
Lie symmetry analysis, conservation laws and solitary wave solutions to a fourth-order nonlinear generalized Boussinesq water wave equation
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DOI：
10.1016/j.aml.2019.106056
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发表时间：
2020-02-01
影响因子：
3.7
通讯作者：
Tian, Shou-Fu
中科院分区：
文献类型：
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作者：
Tian, Shou-Fu
本文研究了四阶非线性广义 Boussinesq 水波方程，该方程描述了浅水中长波的传播。我们采用李对称方法来研究其向量场和最优系统。此外，我们利用最优系统，包括双曲型、三角型、有理型、雅可比椭圆型和Weierstrass椭圆型解，推导了其对称性约简和十二族孤子波解。两个简化方程是类 Painleve 方程。最后，给出了完整的局部守恒定律集，并利用守恒定律乘子进行了详细的推导。 (C) 2019 Elsevier Ltd. 保留所有权利。
A fourth-order nonlinear generalized Boussinesq water wave equation is studied in this work, which describes the propagation of long waves in shallow water. We employ Lie symmetry method to study its vector fields and optimal systems. Moreover, we derive its symmetry reductions and twelve families of soliton wave solutions by using the optimal systems, including hyperbolic-type, trigonometric-type, rational-type, Jacobi elliptic-type and Weierstrass elliptic-type solutions. Two of reduced equations are Painleve-like equations. Finally, the complete set of local conservation laws is presented with a detailed derivation by using the conservation law multiplier. (C) 2019 Elsevier Ltd. All rights reserved.