Geodesic
Exact Solutions for a~Family of Variable-Coefficient ``Reaction--Duffing'' Equations via the B\"acklund Transformation
Teoretičeskaâ i matematičeskaâ fizika, Tome 132 (2002) no. 1, pp. 90-96

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The homogeneous balance method is extended and applied to a class of variable-coefficient “reaction–duffing” equations, and a Bäcklund transformation (BT) is obtained. Based on the BT, a nonlocal symmetry and several families of exact solutions of this equation are obtained, including soliton solutions that have important physical significance. The Fitzhugh–Nagumo and Chaffee–Infante equations are also considered as special cases.
Keywords: “reaction–duffing” equation, Bäcklund transformation, symmetry
Mots-clés : exact solution, soliton solution. 
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     author = {Yong Chen and Zhenya Yan and Hongqing Zhang},
     title = {Exact {Solutions} for {a~Family} of {Variable-Coefficient} {``Reaction--Duffing''} {Equations} via the {B\"acklund} {Transformation}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2002_132_1_a4/}
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Yong Chen; Zhenya Yan; Hongqing Zhang. Exact Solutions for a~Family of Variable-Coefficient ``Reaction--Duffing'' Equations via the B\"acklund Transformation. Teoretičeskaâ i matematičeskaâ fizika, Tome 132 (2002) no. 1, pp. 90-96. http://geodesic.mathdoc.fr/item/TMF_2002_132_1_a4/