Residual Symmetries and Interaction Solutions for the Classical Korteweg-de Vries Equation
-
Jin-Xi Fei
,
Wei-Ping Cao
Abstract
The non-local residual symmetry for the classical Korteweg-de Vries equation is derived by the truncated Painlevé analysis. This symmetry is first localised to the Lie point symmetry by introducing the auxiliary dependent variables. By using Lie’s first theorem, we then obtain the finite transformation for the localised residual symmetry. Based on the consistent tanh expansion method, some exact interaction solutions among different non-linear excitations are explicitly presented finally. Some special interaction solutions are investigated both in analytical and graphical ways at the same time.
Acknowledgments
This work was supported by the Foundation of Educational Committee of Zhejiang Province (grant no. Y201432744), and the Zhejiang Province Natural Science Foundation of China (grant nos. LY14A010005 and LQ14A040001).
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Articles in the same Issue
- Frontmatter
- Hydrogen and Carbon Vapour Pressure Isotope Effects in Liquid Fluoroform Studied by Density Functional Theory
- Analytic Approximations to Nonlinear Boundary Value Problems Modeling Beam-Type Nano-Electromechanical Systems
- Resistance Distances and Kirchhoff Index in Generalised Join Graphs
- Residual Symmetries and Interaction Solutions for the Classical Korteweg-de Vries Equation
- Nanofluidic Transport over a Curved Surface with Viscous Dissipation and Convective Mass Flux
- Reconstruction of f(T) Gravity with Interacting Variable-Generalised Chaplygin Gas and the Thermodynamics with Corrected Entropies
- Peristaltic Flow of Rabinowitsch Fluid in a Curved Channel: Mathematical Analysis Revisited
- Analysis of the Laminar Newtonian Fluid Flow Through a Thin Fracture Modelled as a Fluid-Saturated Sparsely Packed Porous Medium
- Lie Symmetries and Conservation Laws of the Generalised Foam-Drainage Equation
- Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham–Broer–Kaup–Like Equations
- Discrete and Semidiscrete Models for AKNS Equation
