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    Symmetry, Vol. 6, Pages 1026-1036: Benjamin–Bona–Mahony Equation with Variable Coefficients: Conservation Laws (2014)
    MDPI Publishing
    In: Symmetry
    Details
    Publication Date: 2014-12-16
    Description: This paper aims to construct conservation laws for a Benjamin–Bona–Mahony equation with variable coefficients, which is a third-order partial differential equation. This equation does not have a Lagrangian and so we transform it to a fourth-order partial differential equation, which has a Lagrangian. The Noether approach is then employed to construct the conservation laws. It so happens that the derived conserved quantities fail to satisfy the divergence criterion and so one needs to make adjustments to the derived conserved quantities in order to satisfy the divergence condition. The conservation laws are then expressed in the original variable. Finally, a conservation law is used to obtain exact solution of a special case of the Benjamin–Bona–Mahony equation.
    Electronic ISSN: 2073-8994
    Topics: Mathematics , Physics
    Published by MDPI Publishing
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  • 2
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    Conservation Laws for a generalized Ito-type coupled KdV system (2012)
    Springer
    Details
    Publication Date: 2012-12-29
    Description: In this paper, the conservation laws for a generalized Ito-type coupled Korteweg-de Vries (KdV) system are constructed by increasing the order of the partial differential equations. The generalized Ito-type coupled KdV system is athird-order system of two partial differential equations and does not have a Lagrangian. The transformation $u={U_{x}}$, $v={V_{x}}$ converts the generalized Ito-type coupled KdV system to a system of fourth-order partial differential equations in $U$ and $V$ variables, which has a Lagrangian. Noether's approach is then used to construct the conservation laws. Finally, the conservation laws are expressed in the original variables $u$ and $v$. Some local and infinitely many nonlocal conserved quantities are found for the generalized Ito-typed coupled KdV system.
    Print ISSN: 1687-2762
    Electronic ISSN: 1687-2770
    Topics: Mathematics
    Published by Springer
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