### Abstract

It is said that L(x,u, Del u) is a null Lagrangian if and only if the corresponding integral functional E(u)= integral _{Omega}L(x,u, Del u) dx has the property that E(u+ phi )=E(u) For all phi in C_{0} ^{infinity}( Omega ), for any choice of u in C^{1}( Omega ). In the homogeneous case, corresponding to L(x,u, Del u)= Phi ( Del u), it is known that a necessary and sufficient condition for L to be a null Lagrangian is that Phi ( Del u) is an affine combination of subdeterminants of Del u of all orders. The authors show that all inhomogeneous null Lagrangians may be constructed from these homogeneous ones by introducing appropriate potentials.

Original language | English |
---|---|

Article number | 005 |

Pages (from-to) | 389-398 |

Number of pages | 10 |

Journal | Nonlinearity |

Volume | 1 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1988 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Nonlinearity*,

*1*(2), 389-398. [005]. https://doi.org/10.1088/0951-7715/1/2/005

**The structure of null Lagrangians.** / Olver, P. J.; Sivaloganathan, J.

Research output: Contribution to journal › Article

*Nonlinearity*, vol. 1, no. 2, 005, pp. 389-398. https://doi.org/10.1088/0951-7715/1/2/005

}

TY - JOUR

T1 - The structure of null Lagrangians

AU - Olver, P. J.

AU - Sivaloganathan, J.

PY - 1988

Y1 - 1988

N2 - It is said that L(x,u, Del u) is a null Lagrangian if and only if the corresponding integral functional E(u)= integral OmegaL(x,u, Del u) dx has the property that E(u+ phi )=E(u) For all phi in C0 infinity( Omega ), for any choice of u in C1( Omega ). In the homogeneous case, corresponding to L(x,u, Del u)= Phi ( Del u), it is known that a necessary and sufficient condition for L to be a null Lagrangian is that Phi ( Del u) is an affine combination of subdeterminants of Del u of all orders. The authors show that all inhomogeneous null Lagrangians may be constructed from these homogeneous ones by introducing appropriate potentials.

AB - It is said that L(x,u, Del u) is a null Lagrangian if and only if the corresponding integral functional E(u)= integral OmegaL(x,u, Del u) dx has the property that E(u+ phi )=E(u) For all phi in C0 infinity( Omega ), for any choice of u in C1( Omega ). In the homogeneous case, corresponding to L(x,u, Del u)= Phi ( Del u), it is known that a necessary and sufficient condition for L to be a null Lagrangian is that Phi ( Del u) is an affine combination of subdeterminants of Del u of all orders. The authors show that all inhomogeneous null Lagrangians may be constructed from these homogeneous ones by introducing appropriate potentials.

UR - http://www.scopus.com/inward/record.url?scp=6344244957&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/1/2/005

DO - 10.1088/0951-7715/1/2/005

M3 - Article

VL - 1

SP - 389

EP - 398

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 2

M1 - 005

ER -