288,615 research outputs found
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
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
Two-stage Turing model for generating pigment patterns on the leopard and the jaguar
Based on the results of phylogenetic analysis, which showed that flecks are the primitive pattern of the felid family and all other patterns including rosettes and blotches develop from it, we construct a Turing reaction-diffusion model which generates spot patterns initially. Starting from this spotted pattern, we successfully generate patterns of adult leopards and jaguars by tuning parameters of the model in the subsequent phase of patterning
Oscillatory Turing Patterns in a Simple Reaction-Diffusion System
Turing suggested that, under certain conditions, chemicals can react and diffuse in such a way as to produce steady-state inhomogeneous spatial patterns of chemical concentrations. We consider a simple two-variable reaction-diffusion system and find there is a spatio-temporally oscillating solution (STOS) in parameter regions where linear analysis predicts a pure Turing instability and no Hopf instability. We compute the boundary of the STOS and spatially non-uniform solution (SSNS) regions and investigate what features control its behavior
A node-based smoothed conforming point interpolation method (NS-CPIM) for elasticity problems
This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher order conforming PIM shape functions (CPIM) have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch test; (2) provides an upper bound of strain energy; (3) avoid the volumetric locking; (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs
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