Wronskian, Pfaffian and periodic wave solutions for a $$(2 + 1)$$ ( 2 + 1 ) -dimensional extended shallow water wave equation

Wronskian, Pfaffian and periodic wave solutions for a $$(2 + 1)$$ ( 2 + 1 ) -dimensional... Under investigation in this paper is a $$(2 + 1)$$ ( 2 + 1 ) -dimensional extended shallow water wave equation. Bilinear form is obtained via the generalized dependent variable transformation. The Nth-order analytic solutions are, respectively, obtained via the Wronskian and Pfaffian techniques. Soliton solutions are constructed through the Nth-order solutions. Discussions on the propagation of the solitons indicate that the soliton solutions with $$\varphi (y)$$ φ ( y ) are more general than those without $$\varphi (y)$$ φ ( y ) , and $$\varphi (y)$$ φ ( y ) could affect the features of the soliton solutions, where $$\varphi (y)$$ φ ( y ) is a real function related to the aforementioned transformation. One-periodic wave solutions are obtained via the Hirota–Riemann method. Relation between the one-periodic wave solutions and one-soliton solutions is studied, which indicates that the one-periodic wave solutions can approach to the one-soliton solutions under certain condition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Wronskian, Pfaffian and periodic wave solutions for a $$(2 + 1)$$ ( 2 + 1 ) -dimensional extended shallow water wave equation

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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-017-3630-y
Publisher site
See Article on Publisher Site

Abstract

Under investigation in this paper is a $$(2 + 1)$$ ( 2 + 1 ) -dimensional extended shallow water wave equation. Bilinear form is obtained via the generalized dependent variable transformation. The Nth-order analytic solutions are, respectively, obtained via the Wronskian and Pfaffian techniques. Soliton solutions are constructed through the Nth-order solutions. Discussions on the propagation of the solitons indicate that the soliton solutions with $$\varphi (y)$$ φ ( y ) are more general than those without $$\varphi (y)$$ φ ( y ) , and $$\varphi (y)$$ φ ( y ) could affect the features of the soliton solutions, where $$\varphi (y)$$ φ ( y ) is a real function related to the aforementioned transformation. One-periodic wave solutions are obtained via the Hirota–Riemann method. Relation between the one-periodic wave solutions and one-soliton solutions is studied, which indicates that the one-periodic wave solutions can approach to the one-soliton solutions under certain condition.

Journal

Nonlinear DynamicsSpringer Journals

Published: Jul 14, 2017

References

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