Abstract
This paper studies the Zakharov equation with power law nonlinearity. The traveling wave hypothesis is applied to obtain the 1-soliton solution of this equation. The multiplier method from Lie symmetries is subsequently utilized to obtain the conservation laws of the equations. Finally, using the exact 1-soliton solution, the conserved quantities are listed.
Highlights
There are several nonlinear evolution equations (NLEEs) that appears in various areas of applied mathematics and theoretical physics [1,2,3,4,5,6,7,8,9,10,11,12,13]
These NLEEs are a key to the understanding of various physical phenomena that governs the world today
The nonlinear Schrödinger’s equation (NLSE) appears in nonlinear optics, while Korteweg– de Vries (KdV) equation is studied in fluid dynamics and the sine–Gordon equation (SGE) is seen in theoretical physics
Summary
There are several nonlinear evolution equations (NLEEs) that appears in various areas of applied mathematics and theoretical physics [1,2,3,4,5,6,7,8,9,10,11,12,13] These NLEEs are a key to the understanding of various physical phenomena that governs the world today. Some of these commonly studied NLEEs are the nonlinear Schrödinger’s equation (NLSE), Korteweg– de Vries (KdV) equation, sine–Gordon equation (SGE), just to name a few. The conserved quantities will be subsequently computed using the soliton solution by the aid of Lie symmetry analysis
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