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2001 (2)
2000 (1)
1Author    Chandan Kr, A.Roy Das, ChowdhuryRequires cookie*
 Title    Complete Integrability Prolongation Structure and Backlund Transformation for the Konno-Onno Equation  
 Abstract    Painleve analysis is used to study the complete integrability of the recently proposed Konno-Onno equation, which also leads to a general form of solutions of the system. An independent study, using the prolongation theory, gives the explicit form of the Lax pair which is then used to obtain the Backlund transformation connecting two sets of solutions of the system. The existence of the Lax pair and the positive result of the Painleve test indicate the complete integrability of the system. 
  Reference    Z. Naturforsch. 55a, 545—549 (2000); received February 11 2000 
  Published    2000 
  Keywords    Integrability, Backlund Transformation, Prolongation Structure, Lie Algebra 
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 TEI-XML for    default:Reihe_A/55/ZNA-2000-55a-0545.pdf 
 Identifier    ZNA-2000-55a-0545 
 Volume    55 
2Author    Jin-Ping Yinga, Sen-Yue LouaRequires cookie*
 Title    Abundant Coherent Structures of the (2+l)-dimensional Broer-Kaup-Kupershmidt Equation  
 Abstract    By using of the Bäcklund transformation, which is related to the standard truncated Painleve analysis, some types of significant exact soliton solutions of the (2+l)-dimensional Broer-Kaup-Kupershmidt equation are obtained. A special type of soliton solutions may be described by means of the variable coefficient heat conduction equation. Due to the entrance of infinitely many arbitrary functions in the general expressions of the soliton solution the solitons of the (2+1 ^ d i­ mensional Broer-Kaup equation possess very abundant structures. By fixing the arbitrary functions appropriately, we may obtain some types of multiple straight line solitons, multiple curved line solitons, dromions, ring solitons and etc. 
  Reference    Z. Naturforsch. 56a, 619—625 (2001); received November 26 2000 
  Published    2001 
  Keywords    Bäcklund Transformation, (2+l)-dimensional Broer-Kaup-Kupershmidt Equation, Dromion Solution, Ring Solitons 
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 TEI-XML for    default:Reihe_A/56/ZNA-2001-56a-0619.pdf 
 Identifier    ZNA-2001-56a-0619 
 Volume    56 
3Author    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