Power expansions for the selfsimilar solutions of the modified SavadaKotera equation
Abstract
The fourthorder ordinary differential equation, defining new transcendents, is studied. The selfsimilar solutions of the KaupKupershmidt and SavadaKotera equations are shown to be found taking its solutions into account. Equation studied belongs to the class of fourthorder analogues of the Painlevé equations. All the power and nonpower asymptotic forms and expansions near points $z=0$, $z=\infty$ and near arbitrary point $z=z_0$ are found by means of power geometry methods. The exponential additions to the solutions of studied equation are also determined.
 Publication:

arXiv eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:nlin/0606042
 Bibcode:
 2006nlin......6042E
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 31 pages, 9 figures