Nonlinear progressive waves in water of finite depth — an analytic approximation

By Longbin Tao, Hao Song, Subrata Chakrabarti. 2007

63 citations recorded by the source corpus.

An analytical solution using homotopy analysis method is developed to describe the nonlinear progressive waves in water of finite depth. The velocity potential of the wave is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. Unlike the perturbation method, the present approach is not dependent on small parameters. Thus solutions are possible for steep waves. Furthermore, a significant improvement of the convergence rate and region is achieved by applying Homotopy-Pade Approximants. The calculated wave characteristics of the present solution agree well with previous numerical and experimental results.

Subfields: Earth-Surface Processes, Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/12bf4cee1b49d0387f69358de420fb1f7ff5401d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Earth-Surface Processes

1. Magdy A. El-Tawil
2. Shaheed N. Huseen
3. Hany N. Hassan
4. Shijun Liao

In Oceanography

1. Magdy A. El-Tawil
2. Shaheed N. Huseen
3. Hany N. Hassan
4. Shijun Liao

In Statistical and Nonlinear Physics

1. Magdy A. El-Tawil
2. Shaheed N. Huseen
3. Hany N. Hassan
4. Shijun Liao

Citations in the corpus

• THE Q-HOMOTOPY ANALYSIS METHOD (Q-HAM) (2012, methodology): “…more researchers have been successfully applying (HAM) to various nonlinear problems in science and engineering ,such as, the nonlinear water waves (Tao et al. 2007, groundwater flows (Song and Tao 2007) , time-dependent Emden-Fowler type equations (Bataineh et al. 2007) , solving high order…”
• An efficient analytic approach for solving two‐point nonlinear boundary value problems by homotopy analysis method (2011, methodology): “In recent years, this method has been successfully employed to solve many types of nonlinear problems in science and engineering such as the viscous flows of non-Newtonian fluids [3--13], the KdV-type equations [14--18], nonlinear heat transfer [19--21], nonlinear water waves [22], groundwater flows”
• On the relationship between the homotopy analysis method and Euler transform (2010, methodology): “Thereafter, the HAM has been improved step by step [14–20] and has been widely applied in science, engineering and finance [21–29].”
• Homotopy Analysis Method in Nonlinear Differential Equations (2012, background): “Traditionally, perturbation [69,94,95] and asymptotic techn iques are widely applied to obtain analytic approximations of nonlinear problems in sc ien e, finance and engineering.”
• Notes on the homotopy analysis method: Some definitions and theorems (2009, methodology): “Since Liao’s book [21] for the homotopy analysis method was published in 2003, more and more researchers have been successfully applying this method to various nonlinear problems in science and engineering, such as the viscous flows of non-Newtonian fluids [28–38], the KdV-type equations [39–43], no”