Abstract
The aim of this paper is to find the Noether symmetries of a generalized Benney-Luke equation. Thereafter, we construct the associated conserved vectors. In addition, we search for exact solutions for the generalized Benney-Luke equation through the extended tanh method. A brief observation on equations arising from a Lagrangian density function with high order derivatives of the field variables, is also discussed.
Highlights
Benney-Luke Equation (1) models waves propagating on the surface of a fluid in a shallow channel of constant depth taking into consideration the surface tension effect
The vector field X, defined in Equation (2), is a Noether symmetry corresponding to the Lagrangian L(t, x, u, ut, u x, utx, u xx ) of Equation (5) if there exist the gauge terms
We examine and discuss the physical meaning of the derived conservation laws
Summary
Benney-Luke Equation (1) models waves propagating on the surface of a fluid in a shallow channel of constant depth taking into consideration the surface tension effect. We refer the interested reader to references [7,8,9,10,11,12] and references therein. In this present work, our goal is to compute conservation laws and exact solutions of Equation (1). We compute conservation laws of Equation (1) by employing Noether’s theorem. The interested reader is referred to the cited paper for details [13,14].
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