Abstract
We employ the approaches of both dynamical system and numerical simulation to investigate a generalized KdV equation, which is presented by Yin (2012). Some peakon, compacton, solitary wave, smooth periodic wave, and periodic cusp wave solutions are obtained, and the planar graphs of the compactons and the periodic cusp waves are simulated.
Highlights
To study the role of nonlinear dispersion in the formation of patterns in the liquid drop, Rosenau and Hyman [1] showed in a particular generalization of the KdV equation ut which is called K(2, 2) equation
They found some solitary waves with compact support in it, which they called compactons
Denote that h1,2 = −(2c/3)(3g + c2) ∓ (2/3)(2g + c2)√2g + c2 and hs = −β(β2 + 6αβc − 24gα2)/24α3; we present some exact travelling wave solutions of (3) as follows
Summary
To study the role of nonlinear dispersion in the formation of patterns in the liquid drop, Rosenau and Hyman [1] showed in a particular generalization of the KdV equation ut. Their expressions are, respectively, y (φM φ), φm ≤ φ ≤ φs,.
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