Abstract
The nonlinear wave equation of an elastic rod under finite deformation is solved by the extended mapping method. Abundant new exact traveling wave solutions for this equation are obtained, which contain trigonometric function solutions, solitary wave solutions, Jacobian elliptic function solutions, and Weierstrass elliptic function solutions. The method can be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics.
Highlights
In the recent two decades, the studies of the nonlinear wave have made brilliant achievement
We are concerned with studying the nonlinear wave equation of an elastic rod under finite deformation, which was derived by Liu and Zhang [13] in 2006
We use the extended mapping method to construct new solutions of the nonlinear wave equation of an elastic rod under finite deformation. We hope that this technique can be applied to find new solutions of other kinds of nonlinear evolution equations (NLEEs)
Summary
In the recent two decades, the studies of the nonlinear wave have made brilliant achievement. We are concerned with studying the nonlinear wave equation of an elastic rod under finite deformation, which was derived by Liu and Zhang [13] in 2006 They obtained solitary wave solutions for this equation by the hyperbolic secant function finite expansion method. We use the extended mapping method to construct new solutions of the nonlinear wave equation of an elastic rod under finite deformation. We hope that this technique can be applied to find new solutions of other kinds of NLEEs. This paper is organized as follows.
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