Symmetry Properties of a Generalized Korteweg-de Vires Equation and some Explicit Solutions

Details Symmetry Properties of a Generalized Korteweg-de Vires Equation and some Explicit Solutions Symmetry Properties of a Generalized Korteweg-de Vires Equation and some Explicit Solutions

2006-07-30

arxiv.org/abs/math-ph/0607070v1

Int J Mathematics and Mathematical Sciences 2005:13, 2159-2173 (2005)

Physics

Mathematical Physics

Scientific paper

The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invarint solution for it are obtained by means of this technique. Polynomial, trigonometric and elliptic function solutions can be calculated. It is shown that this generalized equation can be reduced to a first-order equation under a particular second-order differential constraint which resembles a Schrodinger equation. For a particular instance in which the constraint is satisfied, the generalized equation is reduced to a quadrature. A condition which ensures that the reciprocal of a solution is also a solution is given, and a first integral to this constraint is found.

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