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We perform Noether classification of the generalised system of coupled (2 + 1)-dimensional hyperbolic equations, namely u tt - u xx - u yy + P (v) = 0 , v tt - v xx - v yy + Q (u) = 0. Besides this we compute conservation laws corresponding to cases that have Noether symmetries for the underlying coupled hyperbolic system. [ABSTRACT FROM AUTHOR]

We carry out a complete Lie symmetry analysis and Noether symmetry classification of the (1 + 1)-dimensional H [ABSTRACT FROM AUTHOR]

This paper aims to compute conservation laws for the 2D Zakharov–Kuznetsov equation using Noether’s approach through an interesting method of increasing the order of the 2D Zakharov–Kuznetsov equation. Moreover, exact solutions for the 2D Zakharov–Kuznetsov equation are obtained using the Kudryashov method and Jacobi elliptic function method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: We classify a generalized coupled Lane–Emden system with respect to the standard first-order Lagrangian according to the Noether point symmetries it admits. First integrals of the various cases which admit Noether point symmetries are then obtained for the generalized coupled Lane–Emden system under consideration. [ABSTRACT FROM AUTHOR]