383,990 research outputs found
Representations and classification of traveling wave solutions to Sinh-G{\"o}rdon equation
Two concepts named atom solution and combinatory solution are defined. The
classification of all single traveling wave atom solutions to Sinh-G{\"o}rdon
equation is obtained, and qualitative properties of solutions are discussed. In
particular, we point out that some qualitative properties derived intuitively
from dynamic system method aren't true. In final, we prove that our solutions
to Sinh-G{\"o}rdon equation include all solutions obtained in the paper[Fu Z T
et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show
how to give some new identities on Jacobian elliptic functions.Comment: 12 pages. accepted by Communications in theoretical physics (Beijing
The classification of traveling wave solutions and superposition of multi-solutions to Camassa-Holm equation with dispersion
Under the traveling wave transformation, Camassa-Holm equation with
dispersion is reduced to an integrable ODE whose general solution can be
obtained using the trick of one-parameter group. Furthermore combining complete
discrimination system for polynomial, the classifications of all single
traveling wave solutions to the Camassa-Holm equation with dispersion is
obtained. In particular, an affine subspace structure in the set of the
solutions of the reduced ODE is obtained. More general, an implicit linear
structure in Camassa-Holm equation with dispersion is found. According to the
linear structure, we obtain the superposition of multi-solutions to
Camassa-Holm equation with dispersion
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