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2001 (2)
1Author    Zhenya YanRequires cookie*
 Title    Abundant New Exact Solutions of the Coupled Potential KdV Equation and the Modified KdV-Type Equation  
 Abstract    Exact solutions of nonlinear evolution equations (NLEEs)in soliton theory and their applications are studied. A powerful method is established to search for exact travelling wave solutions of NLEEs. We chose the coupled potential KdV equation and modified KdV-type equations presented by Foursov to illustrate the approach with the aid of Maple. As a result, eight families of exact solutions of the coupled potential KdV equation and nine families of exact solutions of the modified KdV-type equations are obtained, which contain new kink-like soliton solutions, kink­ shaped solitons, bell-shaped solitons, periodic solutions, rational solutions and singular solitons. The properties of the solutions are shown in figures. 
  Reference    Z. Naturforsch. 56a, 809—815 (2001); received June 25 2001 
  Published    2001 
  Keywords    Coupled Potential KdV Equation, Modified KdV-type Equation, Soliton Solutions, Periodic Solutions, Rational Solutions 
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 TEI-XML for    default:Reihe_A/56/ZNA-2001-56a-0809.pdf 
 Identifier    ZNA-2001-56a-0809 
 Volume    56 
2Author    Zhenya YanRequires cookie*
 Title    Abundant New Multiple Soliton-like Solutions and Rational Solutions of the (2+l)-Dimensional Broer-Kaup Equation  
 Abstract    In this paper we firstly improve the homogeneous balance method due to Wang, which was only used to obtain single soliton solutions o f nonlinear evolution equations, and apply it to (2 + 1)-dimensional Broer-Kaup (BK) equations such that a Backlund transformation is found again. Considering further the obtained Backlund transformation, the relations are deduced among BK eqautions, well-known Burgers equations and linear heat equations. Finally, abundant multiple soliton-like solutions and infinite rational solutions are obtained from the relations. 
  Reference    Z. Naturforsch. 56a, 816—824 (2001); received June 25 2001 
  Published    2001 
  Keywords    (2+l)-dim ensional Broer-Kaup equation, Backlund Transformation, Burgers Equation, Soliton Solution, Rational solution 
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 TEI-XML for    default:Reihe_A/56/ZNA-2001-56a-0816.pdf 
 Identifier    ZNA-2001-56a-0816 
 Volume    56