Nonlinear Differential Equations With Exact Solutions Expressed Via The Weierstrass Function
2004 ◽
Vol 59
(7-8)
◽
pp. 443-454
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Keyword(s):
A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear differential equations have exact solutions which are general solution of the simplest integrable equation. We use the Weierstrass elliptic equation as building block to find a number of nonlinear differential equations with exact solutions. Nonlinear differential equations of the second, third and fourth order with special solutionsexpressed via theWeierstrass function are given. - PACS: 02.30.Hq (Ordinary differential equations)
2016 ◽
Vol 13
(05)
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pp. 1630005
1988 ◽
Vol 38
(1)
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pp. 19-21
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2009 ◽
Vol 139
(5)
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pp. 1017-1035
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2008 ◽
Vol 465
(2102)
◽
pp. 609-629
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2015 ◽
Vol 18
(1)
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pp. 730-753
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