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An Application of the Modified Reductive Perturbation Method to a Generalized Boussinesq Equation
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February 21, 2013
Abstract
In this work, we apply “the modified reductive perturbation method” to the generalized Boussinesq equation and obtain various form of generalized KdV equations as the evolution equations. Seeking a localized travelling wave solutions for these evolution equations we determine the scale parameters g1 and g2, which corresponds to the correction terms in the wave speed, so as to remove the possible secularities that might occur. Depending on the sign and the values of certain parameters the resulting solutions are shown to be a solitary wave or a periodic solution. The suitability of the method is also shown by comparing the results with the exact travelling wave solution for the generalized Boussinesq equation.
Keywords: modified reductive perturbation method; generalized Boussinesq equation; generalized KdV equations
PACS®(2010): 47.35.Fg
Received: 2011-8-26
Accepted: 2012-9-24
Published Online: 2013-2-21
Published in Print: 2013-2-22
©2013 by De Gruyter
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Keywords for this article
modified reductive perturbation method;
generalized Boussinesq equation;
generalized KdV equations
Articles in the same Issue
- Frontmatter
- Vapor Films under Influence of High Heat Fluxes: Nongravity Surface Waves and Film Explosive Disintegration
- Dynamic Constitutive Behavior and Fracture of Lanthanum Metal Subjected to Impact Compression at Different Temperatures and Impact Tension
- An Application of the Modified Reductive Perturbation Method to a Generalized Boussinesq Equation
- Switching Design for the Asymptotic Stability and Stabilization of Nonlinear Uncertain Stochastic Discrete-time Systems
- A Novel Two-fluid Model for the Identification of Possible Multiple Solutions in Slightly Inclined Pipelines
- Adaptive Synchronization of Filippov Systems with Unknown Parameters via Sliding Mode Control
- Chebyshev Split-step Scheme for the Sine-Gordon Equation in 2+1 Dimensions
- The Numerical Connection between Map and its Differential Equation: Logistic and Other Systems
- Exact Travelling Wave Solutions for the Modified Fornberg-Whitham Equation
