## 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…

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…

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

- Mathematics
- 2018

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…

On the nonlinear self-adjointness of a class of fourth-order evolution equations

- MathematicsAppl. Math. Comput.
- 2016

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…

A family of homogeneous equations: integrable members, Lax pairs and peakon solutions

- Mathematics
- 2016

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits…

Strict self-adjointness and shallow water models

- Mathematics
- 2013

We consider a class of third order equations from the point of view of strict self-adjointness. Necessary and sufficient conditions to the investigated class be strictly self-adjoint are obtained.…

## References

SHOWING 1-10 OF 36 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…

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…

Symmetries and conservation laws for differential equations of mathematical physics

- Mathematics, Physics
- 1999

Ordinary differential equations First-order equations The theory of classical symmetries Higher symmetries Conservation laws Nonlocal symmetries From symmetries of partial differential equations…

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…

Conserved densities for nonlinear evolution equations. I. Even order case

- Mathematics
- 1979

This paper extends to nonlinear evolution equations of odd order the analysis of existence and structure of the polynomial conserved densities. The results for low order densities are similar to the…

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…