Conservation laws and normal forms of evolution equations

@article{Popovych2010ConservationLA,
  title={Conservation laws and normal forms of evolution equations},
  author={Roman O. Popovych and Artur Sergyeyev},
  journal={Physics Letters A},
  year={2010},
  volume={374},
  pages={2210-2217}
}
View PDF on arXiv
35 Citations
Background Citations
18
Methods Citations
1
Results Citations
1

35 Citations

Simplest potential conservation laws of linear evolution equations

Every simplest potential conservation law of any (1+1)-dimensional linear evolution equation of even order proves induced by a local conservation law of the same equation. This claim is true also for…

Symmetries and conservation laws for a generalization of Kawahara equation

Inverse problem on conservation laws

Conservation laws and symmetries of time-dependent generalized KdV equations

A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equations, a corresponding…

Linearizability for third order evolution equations

The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary…

Conservation Laws and Nonlocal Variables

We discuss here the notion of conservation laws and briefly the theory of Abelian coverings over infinitely prolonged equations. Computation of conservation laws is also closely related to that of…

Generalized symmetries and conservation laws of (1 + 1)-dimensional Klein–Gordon equation

Using advantages of nonstandard computational techniques based on the light-cone variables, we explicitly find the algebra of generalized symmetries of the (1+1)-dimensional Klein-Gordon equation.…

Nonlocal symmetry analysis and conservation laws to an third-order Burgers equation

The nonlocal residual symmetry related to truncated Painlevé expansion of third-order Burgers equation is performed. Then, the potential symmetries of the equation are derived; on the basis of…

A family of wave equations with some remarkable properties

TLDR
Recursion operators are found for two members of the family investigated and a Lax pair is obtained, proving its complete integrability, and peakon-type solutions are also found for a certain choice of the parameters.

Nonlinear self-adjointness and conservation laws

The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict…

References

SHOWING 1-10 OF 34 REFERENCES

Conservation Laws of Evolution Equations: Generic Non-existence

Evolution-type partial differential equations in one space variable are formulated in terms of exterior differential systems. The space of conservation laws is discussed in this geometric context,…

Third-order scalar evolution equations with conservation laws

Abstract. Associated to the family of third-order quasilinear scalar evolution equations is the geometry of point transformations. This geometry provides a framework from which to study the structure…

Local conservation laws of second-order evolution equations

Generalizing results by Bryant and Griffiths (1995 Duke Math. J. 78 531), we completely describe local conservation laws of second-order (1 + 1)-dimensional evolution equations up to contact…

Conservation Laws and Non-Lie Symmetries for Linear PDEs

Abstract We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are…

Classification of conservation laws for KdV-like equations

Conserved densities for linear evolution systems

A general discussion of the conservation laws for simple linear evolution systems is presented. The analysis is based upon an extension of the Gel'fand-Dikii symbolic algorithm to cover…

Hierarchy of conservation laws of diffusion-convection equations

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible…

Conservation Laws and Potential Symmetries of Linear Parabolic Equations

Abstract We carry out an extensive investigation of conservation laws and potential symmetries for the class of linear (1+1)-dimensional second-order parabolic equations. The group classification of…

Potential conservation laws

We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure…

Korteweg‐de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion

With extensive use of the nonlinear transformations presented in Paper I of the series, a variety of conservation laws and constants of motion are derived for the Korteweg‐de Vries and related…