On elliptic solutions of nonlinear ordinary differential equations

The problem of constructing and classifying exact elliptic solutions of autonomous nonlinear ordinary differential equations is studied. An algorithm for finding elliptic solutions in explicit form is presented.

[1]  E. Fan,et al.  Extended tanh-function method and its applications to nonlinear equations , 2000 .

[2]  Nikolay A. Kudryashov,et al.  From Laurent series to exact meromorphic solutions: The Kawahara equation , 2010, 1112.5266.

[3]  Y. Bagderina Rational solutions of fifth-order evolutionary equations for describing waves on water , 2008 .

[4]  N. A. Kudryashov,et al.  Partial differential equations with solutions having movable first-order singularities , 1992 .

[5]  Anjan Biswas,et al.  Solitary wave solution for the generalized Kawahara equation , 2009, Appl. Math. Lett..

[6]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[7]  Paul Abbott,et al.  The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations , 2002 .

[8]  N. Kudryashov,et al.  Polygons of differential equations for finding exact solutions , 2007 .

[9]  Nikolai A. Kudryashov,et al.  Exact solutions of the generalized Kuramoto-Sivashinsky equation , 1990 .

[10]  Nikolay A. Kudryashov,et al.  Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations , 2011, 1112.5445.

[11]  Nikolai A. Kudryashov,et al.  On types of nonlinear nonintegrable equations with exact solutions , 1991 .

[12]  S. Vernov Proof of the Absence of Elliptic Solutions of the Cubic Complex Ginzburg-Landau Equation , 2006 .

[13]  Zuntao Fu,et al.  New transformations and new approach to find exact solutions to nonlinear equations , 2002 .

[14]  Nikolai A. Kudryashov,et al.  Extended simplest equation method for nonlinear differential equations , 2008, Appl. Math. Comput..

[15]  N. A. Kudryashov Simplest equation method to look for exact solutions of nonlinear differential equations , 2005 .