摘要Employing the compatibility method, we obtain the symmetries of the (3+1)-dimensional Kadomtsev--Petviashvili (KP) equation. Four types of similarity reductions of the KP equation are obtained by solving the corresponding characteristic equations associated with symmetry equations. In addition, a lot of similarity solutions to the KP equation are obtained.
Abstract：Employing the compatibility method, we obtain the symmetries of the (3+1)-dimensional Kadomtsev--Petviashvili (KP) equation. Four types of similarity reductions of the KP equation are obtained by solving the corresponding characteristic equations associated with symmetry equations. In addition, a lot of similarity solutions to the KP equation are obtained.
LIU Na;LIU Xi-Qiang. Similarity Reductions and Similarity Solutions of the (3+1)-Dimensional Kadomtsev--Petviashvili Equation[J]. 中国物理快报, 2008, 25(10): 3527-3530.
LIU Na, LIU Xi-Qiang. Similarity Reductions and Similarity Solutions of the (3+1)-Dimensional Kadomtsev--Petviashvili Equation. Chin. Phys. Lett., 2008, 25(10): 3527-3530.
[1] El-Wakil S A et al 2007 Chaos, Solitons &Fractals 31 840 [2] Bai C L et al 2006 Chaos, Solitons & Fractalsbf 27 1026 [3] Wazwaz A M 2007 Appl. Math. Comput. bf 184 1002 [4] He J H et al 2006 Chaos, Solitons & Fractals bf30 700 [5] Fan E G and Zhang J 2002 Phys. Lett. A bf 305383 [6] Abdou M A 2007 Chaos, Solitons & Fractals bf31 95 [7] Ren Y J et al 2006 Chaos, Solitons & Fractalsbf 27 959 [8] Yan Z L and Liu X Q 2006 Appl. Math. Comput. bf180 288 [9] Zhang S L et al 2002 Chin.Phys.Lett bf 19 1741 [10] Zhang S L et al 2003 J. Phys. A: Math. Genbf 36 12223 [11] Swnatorski A and Infeld E 1996 Phys. Rev. Lett.bf 77 2855 [12] Chen Y et al 2003 Phys. Lett. A bf 307 107 [13] EI-Sayed S M et al 2004 Appl. Math. Comput. bf157 523 [14] Hu J Q 2005 Chaos Solitons & Fractals bf 23391 [15] Chen H T et al 2004 Appl. Math. Comput. bf 157765 [16] Liu G T and Fan T Y 2005 Phys. Lett. A bf 345161 [17] Lou S Y et al 2006 Chaos Solitons & Fractalsbf 30 804 [18] Zhang H Q 2007 Commun. Nonlinear. Sci. Numer.Simulat. bf 12 627
2008, Vol. 25 
