The Modified Simple Equation Method, the Exp-Function Method, and the Method of Soliton Ansatz for Solving the Long–Short Wave Resonance Equations
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E.M.E. Zayed
Abstract
The modified simple equation method, the exp-function method, and the method of soliton ansatz for solving nonlinear partial differential equations are presented. Based on these three different methods, we obtain the exact solutions and the bright–dark soliton solutions with parameters of the long-short wave resonance equations which describe the resonance interaction between the long wave and the short wave. When these parameters take special values, the solitary wave solutions are derived from the exact solutions. We compare the results obtained using the three methods. Also, a comparison between our results and the well-known results is given.
Acknowledgments
The authors wish to thank the referees for their comments on this paper.
References
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©2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation
- The Modified Simple Equation Method, the Exp-Function Method, and the Method of Soliton Ansatz for Solving the Long–Short Wave Resonance Equations
- Application of the Reverberation-Ray Matrix to the Non-Fourier Heat Conduction in Functionally Graded Materials
- Rational Solutions for Lattice Potential KdV Equation and Two Semi-discrete Lattice Potential KdV Equations
- Structural, Electronic, Magnetic and Optical Properties of Ni,Ti/Al-based Heusler Alloys: A First-Principles Approach
- Ab Initio Calculations on the Structural, Mechanical, Electronic, Dynamic, and Optical Properties of Semiconductor Half-Heusler Compound ZrPdSn
- Qualitative Behaviour of Generalised Beddington Model
- Studying Nuclear Level Densities of 238U in the Nuclear Reactions within the Macroscopic Nuclear Models
- Total π-Electron Energy of Conjugated Molecules with Non-bonding Molecular Orbitals
- Investigation of Thermal Expansion and Physical Properties of Carbon Nanotube Reinforced Nanocrystalline Aluminum Nanocomposite
- Bistable Bright Optical Spatial Solitons due to Charge Drift and Diffusion of Various Orders in Photovoltaic Photorefractive Media Under Closed-Circuit Conditions
- Application of a Differential Transform Method to the Transient Natural Convection Problem in a Vertical Tube with Variable Fluid Properties
Articles in the same Issue
- Frontmatter
- Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation
- The Modified Simple Equation Method, the Exp-Function Method, and the Method of Soliton Ansatz for Solving the Long–Short Wave Resonance Equations
- Application of the Reverberation-Ray Matrix to the Non-Fourier Heat Conduction in Functionally Graded Materials
- Rational Solutions for Lattice Potential KdV Equation and Two Semi-discrete Lattice Potential KdV Equations
- Structural, Electronic, Magnetic and Optical Properties of Ni,Ti/Al-based Heusler Alloys: A First-Principles Approach
- Ab Initio Calculations on the Structural, Mechanical, Electronic, Dynamic, and Optical Properties of Semiconductor Half-Heusler Compound ZrPdSn
- Qualitative Behaviour of Generalised Beddington Model
- Studying Nuclear Level Densities of 238U in the Nuclear Reactions within the Macroscopic Nuclear Models
- Total π-Electron Energy of Conjugated Molecules with Non-bonding Molecular Orbitals
- Investigation of Thermal Expansion and Physical Properties of Carbon Nanotube Reinforced Nanocrystalline Aluminum Nanocomposite
- Bistable Bright Optical Spatial Solitons due to Charge Drift and Diffusion of Various Orders in Photovoltaic Photorefractive Media Under Closed-Circuit Conditions
- Application of a Differential Transform Method to the Transient Natural Convection Problem in a Vertical Tube with Variable Fluid Properties
