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The tanh method: I. Exact solutions of nonlinear evolution and wave equations
A systemized version of the tanh method is used to solve particular evolution and wave equations. If one deals with conservative systems, one seeks travelling wave solutions in the form of a finiteExpand
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The tanh method: II. Perturbation technique for conservative systems
With the aid of the tanh method, nonlinear wave equations are solved in a perturbative way. First, the KdVBurgers equation is investigated in the limit of weak dispersion. As a result, a generalExpand
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Symbolic methods to construct exact solutions of nonlinear partial differential equations
Two straightforward methods for finding solitary-wave and soliton solutions are presented and applied to a variety of nonlinear partial differential equations. The first method is a simplied versionExpand
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Symbolic Computation of Conserved Densities for Systems of Nonlinear Evolution Equations
A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. Expand
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Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA
The direct algebraic method for constructing travelling wave solutions on nonlinear evolution and wave equations has been generalized and systematized. The class of solitary wave solutions isExpand
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Review of symbolic software for lie symmetry analysis
Computer algebra packages and tools that aid in the computation of Lie symmetries of differential equations are reviewed. The methods and algorithms of Lie symmetry analysis are briefly outlined.Expand
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Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method
The authors present a systematic and formal approach toward finding solitary wave solutions of nonlinear evolution and wave equations from the real exponential solutions of the underlying linearExpand
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Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs
New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi’s elliptic functions. Expand
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Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations
A new algorithm is presented to find exact traveling wave solutions of differential–difference equations in terms of tanh functions. Expand
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