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}
}
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35 Citations
Background Citations
19
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…
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Conservation Laws and Nonlocal Variables
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Generalized symmetries and conservation laws of (1 + 1)-dimensional Klein–Gordon equation
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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…
On the nonlinear self-adjointness of a class of fourth-order evolution equations
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…
A family of homogeneous equations: integrable members, Lax pairs and peakon solutions
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
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.…
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References

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