Prolongation Structure of a Generalised Inhomogeneous Gardner Equation in Plasmas and Fluids
-
Xi-Yang Xie
,
Wen-Rong Sun
Abstract
In this article, the prolongation structure technique is applied to a generalised inhomogeneous Gardner equation, which can be used to describe certain physical situations, such as the stratified shear flows in ocean and atmosphere, ion acoustic waves in plasmas with a negative ion, interfacial solitary waves over slowly varying topographies, and wave motion in a non-linear elastic structural element with large deflection. The Lax pairs, which are derived via the prolongation structure, are more general than the Lax pairs published before. Under the Painlevé conditions, the linear-damping coefficient equals to zero, the quadratic non-linear coefficient is proportional to the dispersive coefficient c(t), the cubic non-linear coefficient is proportional to c(t), leaving no constraints on c(t) and the dissipative coefficient d(t). We establish the prolongation structure through constructing the exterior differential system. We introduce two methods to obtain the Lax pairs: (a) based on the prolongation structure, the Lax pairs are obtained, and (b) via the Lie algebra, we can derive the Pfaffian forms and Lax pairs when certain parameters are chosen. We set d(t) as a constant to discuss the influence of c(t) on the Pfaffian forms and Lax pairs, and to discuss the influence of d(t) on the Pfaffian forms and Lax pairs, we set c(t) as another constant. Then, we get different prolongation structure, Pfaffian forms and Lax pairs.
Acknowledgments
This work has been supported by the National Natural Science Foundation of China under Grant No. 11272023, by the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.
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©2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters
- Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation
- Electrical Conduction in Transition-Metal Salts
- Importance of Unit Cells in Accurate Evaluation of the Characteristics of Graphene
- Understanding the Formation Mechanism of Two-Dimensional Atomic Islands on Crystal Surfaces by the Condensing Potential Model
- The Thermodynamic Functions in Curved Space of Neutron Star
- Spanning Trees of the Generalised Union Jack Lattice
- Prolongation Structure of a Generalised Inhomogeneous Gardner Equation in Plasmas and Fluids
- Negative Energies in the Dirac Equation
- Residual Symmetry and Explicit Soliton–Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV–mKdV Equation
- Multifold Darboux Transformations of the Extended Bigraded Toda Hierarchy
- Unidirectional Excitation of Graphene Plasmon in Attenuated Total Reflection (ATR) Configuration
- Completed Optimised Structure of Threonine Molecule by Fuzzy Logic Modelling
Articles in the same Issue
- Frontmatter
- Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters
- Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation
- Electrical Conduction in Transition-Metal Salts
- Importance of Unit Cells in Accurate Evaluation of the Characteristics of Graphene
- Understanding the Formation Mechanism of Two-Dimensional Atomic Islands on Crystal Surfaces by the Condensing Potential Model
- The Thermodynamic Functions in Curved Space of Neutron Star
- Spanning Trees of the Generalised Union Jack Lattice
- Prolongation Structure of a Generalised Inhomogeneous Gardner Equation in Plasmas and Fluids
- Negative Energies in the Dirac Equation
- Residual Symmetry and Explicit Soliton–Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV–mKdV Equation
- Multifold Darboux Transformations of the Extended Bigraded Toda Hierarchy
- Unidirectional Excitation of Graphene Plasmon in Attenuated Total Reflection (ATR) Configuration
- Completed Optimised Structure of Threonine Molecule by Fuzzy Logic Modelling
