Abstract
We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and (2+1)-dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the (2+1)-dimensional Davey-Stewartson equations.
Highlights
Most nonlinear physical phenomena that appear in many areas of scientific fields such as plasma physics, solid state physics, fluid dynamics, optical fibers, mathematical biology, and chemical kinetics can be modelled by nonlinear partial differential equations NLPDEs
The investigation of exact travelling wave solutions of these NLPDEs is important for the understanding of most nonlinear physical phenomena and possible applications
We studied two systems of nonlinear partial differential equations
Summary
Most nonlinear physical phenomena that appear in many areas of scientific fields such as plasma physics, solid state physics, fluid dynamics, optical fibers, mathematical biology, and chemical kinetics can be modelled by nonlinear partial differential equations NLPDEs. We employ the Lie symmetry method and the travelling wave variable approach to obtain exact solutions to both these systems. Sophus Lie 1842–1899 , with the inspiration from Galois’ theory for solving algebraic equations, discovered this method which is known today as Lie group analysis. He showed that many of the known methods of integration of ordinary differential equations could be derived in a systematic manner using his theory of continuous transformation groups. The travelling wave variable approach converts the NLPDEs into a nonlinear ordinary differential equations and is often useful in obtaining exact solutions of the partial differential equations
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