149 research outputs found
A type of bounded traveling wave solutions for the Fornberg-Whitham equation
In this paper, by using bifurcation method, we successfully find the
Fornberg-Whitham equation has a type of traveling wave solutions called
kink-like wave solutions and antikinklike wave solutions. They are defined on
some semifinal bounded domains and possess properties of kink waves and
anti-kink waves. Their implicit expressions are obtained. For some concrete
data, the graphs of the implicit functions are displayed, and the numerical
simulation is made. The results show that our theoretical analysis agrees with
the numerical simulation.Comment: 14 pages, 10 figure
Solitons, peakons, and periodic cuspons of a generalized Degasperis-Procesi equation
We employ the bifurcation theory of planar dynamical systems to investigate
the exact travelling wave solutions of a generalized Degasperis-Procesi
equation. The implicit expression of smooth soliton solutions is given. The
explicit expressions of peaked soliton solutions and periodic cuspon solutions
are also obtained. Further, we show the relationship among the smooth soliton
solutions, the peaked soliton solutions, and the periodic cuspon solutions. The
physical relevance of the found solutions and the reasonwhy these solutions can
exist in this equation are also given.Comment: 14 pages, 41 figure
Soliton and periodic wave solutions to the osmosis K(2, 2) equation
In this paper, two types of traveling wave solutions to the osmosis K(2, 2)
equation are investigated. They are characterized by two parameters. The
expresssions for the soliton and periodic wave solutions are obtained.Comment: 14 pages, 16 figure
Soliton solution of the osmosis K(2, 2) equation
In this Letter, by using the bifurcation method of dynamical systems, we
obtain the analytic expressions of soliton solution of the osmosis K(2, 2)
equation.Comment: 8 page
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