## 35 Citations

### Simplest potential conservation laws of linear evolution equations

- Mathematics, Physics
- 2010

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

- MathematicsJournal of Geometry and Physics
- 2020

### Conservation laws and symmetries of time-dependent generalized KdV equations

- Physics
- 2017

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

- Mathematics
- 2016

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

- Mathematics
- 2017

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

- MathematicsJournal of Mathematical Physics
- 2020

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

- Mathematics, Physics
- 2016

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

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2018

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

- Mathematics
- 2011

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

- Mathematics, Physics
- 1999

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

- Mathematics
- 2002

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

- Mathematics
- 2008

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

- Mathematics
- 2008

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…

### Conserved densities for linear evolution systems

- Mathematics
- 1981

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

- Mathematics
- 2005

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

- Mathematics
- 2008

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

- Mathematics
- 2008

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

- Mathematics
- 1968

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…