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Partially Integrable PTSymmetric Hierarchies of Some Canonical Nonlinear Partial Differential Equations
 Date Issued:
 2013
 Abstract/Description:
 We generalize the work of Bender and coworkers to derive new partiallyintegrable hierarchies of various PTsymmetric, nonlinear partial differential equations. The possible integrable members are identified employing the Painlev(&)#232; Test, a necessary but not sufficient integrability condition, and are indexed by the integer n, corresponding to the negative of the order of the dominant pole in the singular part of the Painlev(&)#232; expansion for the solution.For the PTsymmetric KdV equation, as with some other hierarchies, the first or n=1 equation fails the test, the n=2 member corresponds to the regular KdV equation, while the remainder form an entirely new, possibly integrable hierarchy. Integrability properties of the n=3 and n=4 members, typical of partiallyintegrable systems, including B(&)#228;cklund Transformations, a 'nearLax Pair', and analytic solutions are derived. The solutions, or solitary waves, prove to be algebraic in form, and the extended homogeneous balance technique appears to be the most efficient in exposing the Lax Pair.The PTsymmetric Burgers' equation fails the Painlev(&)#232; Test for its n=2 case, but special solutions are nonetheless obtained. Also, PTsymmetric hierarchies of 2+1 Burgers' and KadomtsevPetviashvili equations, which may prove useful in applications, are analyzed. Extensions of the Painlev(&)#232; Test and Invariant Painlev(&)#232; analysis to 2+1 dimensions are utilized, and BTs and special solutions are found for those cases that pass the Painlev(&)#232; Test.
Title:  Partially Integrable PTSymmetric Hierarchies of Some Canonical Nonlinear Partial Differential Equations. 
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Name(s): 
Pecora, Keri, Author Choudhury, Sudipto, Committee Chair Schober, Constance, Committee Member Rollins, David, Committee Member Christodoulides, Demetrios, Committee Member University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2013  
Publisher:  University of Central Florida  
Language(s):  English  
Abstract/Description:  We generalize the work of Bender and coworkers to derive new partiallyintegrable hierarchies of various PTsymmetric, nonlinear partial differential equations. The possible integrable members are identified employing the Painlev(&)#232; Test, a necessary but not sufficient integrability condition, and are indexed by the integer n, corresponding to the negative of the order of the dominant pole in the singular part of the Painlev(&)#232; expansion for the solution.For the PTsymmetric KdV equation, as with some other hierarchies, the first or n=1 equation fails the test, the n=2 member corresponds to the regular KdV equation, while the remainder form an entirely new, possibly integrable hierarchy. Integrability properties of the n=3 and n=4 members, typical of partiallyintegrable systems, including B(&)#228;cklund Transformations, a 'nearLax Pair', and analytic solutions are derived. The solutions, or solitary waves, prove to be algebraic in form, and the extended homogeneous balance technique appears to be the most efficient in exposing the Lax Pair.The PTsymmetric Burgers' equation fails the Painlev(&)#232; Test for its n=2 case, but special solutions are nonetheless obtained. Also, PTsymmetric hierarchies of 2+1 Burgers' and KadomtsevPetviashvili equations, which may prove useful in applications, are analyzed. Extensions of the Painlev(&)#232; Test and Invariant Painlev(&)#232; analysis to 2+1 dimensions are utilized, and BTs and special solutions are found for those cases that pass the Painlev(&)#232; Test.  
Identifier:  CFE0004736 (IID), ucf:49843 (fedora)  
Note(s): 
20130501 Ph.D. Sciences, Mathematics Doctoral This record was generated from author submitted information. 

Subject(s):  ptsymmetric  painleve  
Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0004736  
Restrictions on Access:  campus 20160515  
Host Institution:  UCF 