Abundant New Exact Solutions of the Coupled Potential KdV Equation and the Modified KdV-Type Equation
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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.
2016 ◽
Vol 2016
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pp. 1-9
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2016 ◽
Vol 71
(8)
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pp. 703-713
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2014 ◽
Vol 548-549
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pp. 1196-1200
2001 ◽
Vol 56
(12)
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pp. 816-824
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2005 ◽
Vol 19
(28n29)
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pp. 1703-1706
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2015 ◽
Vol 70
(7)
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pp. 559-566
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