Group Analysis of the Novikov Equation

Abstract

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions.

References in corpus (4)

• Nonlinear self-adjointness and conservation laws
• Nonlinear self-adjointness in constructing conservation laws
• A New Integrable Equation with Peakon Solutions
• New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order

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• Wave breaking for shallow water models with time decaying solutions
• Integrability, existence of global solutions and wave breaking criteria for a generalization of the Camassa-Holm equation
• Structural and qualitative properties of a geometrically integrable equation
• A generalised multicomponent system of Camassa-Holm-Novikov equations
• Closed-form solutions of Lucas-Uzawa model with externalities via partial Hamiltonian approach