Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-02-18
Nonlinear Sciences
Exactly Solvable and Integrable Systems
A discussion about singularity and some references are added. To appear in Physica Scripta
Scientific paper
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic elliptic integral function and doubly-periodic Jacobian elliptic functions. The derived new solutions include rational, periodic, singular and solitary wave solutions. An interesting comparison with the canonical procedure is provided. In some cases the obtained elliptic solution has singularity at certain region in the whole space. For such solutions we have computed the effective region where the obtained solution is free from such a singularity.
Bagchi Bijan
Das Supratim
Ganguly Asish
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