A Study of Higher Order Terms in Shallow Water Waves via Modified PLK Method
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Hilmi Demiray
Abstract
In this work, by utilizing the modified PLK (Poincare-Lighthill-Kou) method, we studied the propagation of weakly nonlinear waves in a shallow water theory and obtained the Korteweg-deVries (KdV) and the linearized KdV equations with non-homogeneous term as the governing equations of various order terms in the perturbation expansion. The result obtained here is exactly the same with that of Kodama and Taniuti [6], who employed the so-called “re-normalization method”. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. The result obtained here is consistent with the results of Demiray [12], wherein the modified reductive perturbation method had been utilized.
©2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Self-excited Oscillations and Fuel Control of a Combustion Process in a Rijke Tube
- Synchronization of Strictly Different Hyperchaotic Systems with Uncertain Parameters and Models
- Modeling of Synthetic Turbulence Generation in Boundary Layer by Using Zonal RANS/LES Method
- A Meshless Method of Lines for Numerical Solution of Some Coupled Nonlinear Evolution Equations
- A Study of Higher Order Terms in Shallow Water Waves via Modified PLK Method
- Numerical Simulation of Stochastic Inverse Problems in Rigid-Poro-Plastic Materials
- Analytic Investigation of a Reaction-diffusion Brusselator Model with the Time-space Fractional Derivative
- Validation of CE/SE Scheme in Low Mach Number Direct Aeroacoustic Simulation
Articles in the same Issue
- Frontmatter
- Self-excited Oscillations and Fuel Control of a Combustion Process in a Rijke Tube
- Synchronization of Strictly Different Hyperchaotic Systems with Uncertain Parameters and Models
- Modeling of Synthetic Turbulence Generation in Boundary Layer by Using Zonal RANS/LES Method
- A Meshless Method of Lines for Numerical Solution of Some Coupled Nonlinear Evolution Equations
- A Study of Higher Order Terms in Shallow Water Waves via Modified PLK Method
- Numerical Simulation of Stochastic Inverse Problems in Rigid-Poro-Plastic Materials
- Analytic Investigation of a Reaction-diffusion Brusselator Model with the Time-space Fractional Derivative
- Validation of CE/SE Scheme in Low Mach Number Direct Aeroacoustic Simulation
