Abstract
We study the generalized (2+1)-Zakharov-Kuznetsov (ZK) equation of time dependent variable coefficients from the Lie group-theoretic point of view. The Lie point symmetry generators of a special form of the class of equations are derived. We classify the Lie point symmetry generators to obtain the optimal system of onedimensional subalgebras of the Lie symmetry algebras. These subalgebras are then used to construct a number of symmetry reductions and exact group-invariant solutions to the underlying equation.
Highlights
The study of the exact solutions of nonlinear evolution equations plays an important role to understand the nonlinear physical phenomena which are described by these equations
The importance of deriving such exact solutions to these nonlinear equations facilitate the verification of numerical methods and helps in the stability analysis of solutions
We study the exact solutions of one such nonlinear evolution equation, the generalized (2+1)-Zakharov-Kuznetsov equation of the form ut f (t)uux g(t)uxxx h(t)uxyy 0 (1)
Summary
The study of the exact solutions of nonlinear evolution equations plays an important role to understand the nonlinear physical phenomena which are described by these equations. The importance of deriving such exact solutions to these nonlinear equations facilitate the verification of numerical methods and helps in the stability analysis of solutions. We study the exact solutions of one such nonlinear evolution equation, the generalized (2+1)-Zakharov-Kuznetsov equation of the form ut f (t)uux g(t)uxxx h(t)uxyy 0. F(t), g(t) and h(t) are arbitrary smooth functions of the variable t and fgh 0. The equation (1) appears in different forms in many areas of Physics, Applied Mathematics and Engineering (see for example [2, 3])
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