Symmetries of a class of Nonlinear Third Order Partial Differential Equations

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

22 pages, tex, Mathematical and Computer Modelling (to appear)

Scientific paper

In this paper we study symmetry reductions of a class of nonlinear third order partial differential equations $u_t -\epsilon u_{xxt} +2\kappa u_x= u u_{xxx} +\alpha u u_x +\beta u_x u_{xx}$ where $\epsilon$, $\kappa$, $\alpha$ and $\beta$ are arbitrary constants. Three special cases of equation (1) have appeared in the literature, up to some rescalings. In each case the equation has admitted unusual travelling wave solutions: the Fornberg-Whitham equation, for the parameters $\epsilon=1$, $\alpha=-1$, $\beta=3$ and $\kappa=\tfr12$, admits a wave of greatest height, as a peaked limiting form of the travelling wave solution; the Rosenau-Hyman equation, for the parameters $\epsilon=0$, $\alpha=1$, $\beta=3$ and $\kappa=0$, admits a ``compacton'' solitary wave solution; and the Fuchssteiner-Fokas-Camassa-Holm equation, for the parameters $\epsilon=1$, $\alpha=-3$ and $\beta=2$, has a ``peakon'' solitary wave solution. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Symmetries of a class of Nonlinear Third Order Partial Differential Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Symmetries of a class of Nonlinear Third Order Partial Differential Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symmetries of a class of Nonlinear Third Order Partial Differential Equations will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-356132

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.