Equivalence Groupoid and Enhanced Group Classification of a Class of Generalized Kawahara Equations

@article{Vaneeva2020EquivalenceGA,
  title={Equivalence Groupoid and Enhanced Group Classification of a Class of Generalized Kawahara Equations},
  author={Olena O. Vaneeva and Olena Magda and Alexander Zhalij},
  journal={Springer Proceedings in Mathematics \& Statistics},
  year={2020}
}
Transformation properties of a class of generalized Kawahara equations with time-dependent coefficients are studied. We construct the equivalence groupoid of the class and prove that this class is not normalized but can be presented as a union of two disjoint normalized subclasses. Using the obtained results and properly gauging the arbitrary elements of the class, we carry out its complete group classification, which covers gaps in the previous works on the subject. 

References

SHOWING 1-10 OF 17 REFERENCES

Admissible Transformations and Normalized Classes of Nonlinear Schrödinger Equations

The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of

Group analysis of general Burgers–Korteweg–de Vries equations

The complete group classification problem for the class of (1+1)-dimensional rth order general variable-coefficient Burgers–Korteweg–de Vries equations is solved for arbitrary values of r greater

Group analysis of a class of nonlinear Kolmogorov equations

A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group

On form-preserving point transformations of partial differential equations

New identities are presented relating arbitrary order partial derivatives of and for the general point transformation , . These identities are used to study the nature of those point transformations

Symmetry preserving parameterization schemes

Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and

The Symmetry Approach to Classification of Integrable Equations

In this volume each of the contributors proposes his own test to recognize integrable PDEs. We believe that, independently from the basic definition of integrability, the test must satisfy some

Kawahara equation and modified Kawahara equation with time dependent coefficients: symmetry analysis and generalized ‐expansion method

In this paper, variable coefficients Kawahara equation (VCKE) and variable coefficients modified Kawahara equation (VCMKE), which arise in modeling of various physical phenomena, are studied by Lie