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This paper is concerned with the number and distributions of limit cycles in a Z2-equivariant quintic planar vector field. By applying qualitative analysis method of differential equation, we find that 28 limit cycles with four different configurations appear in this special planar polynomial system. It is concluded that H(5) ≥ 28 = 5 + 3, where H(5) is the(More)
The generalized Camassa-Holm equation ut + 2kux − uxxt + auux = 2uxuxx + uuxxx + γuxxx is considered in this paper. Under traveling wave variable substitution, the equation is related to a planar singular system. By making a transformation this singular system becomes a regular system. Through discussing the dynamical behavior of the regular system, the(More)
Under the traveling wave transformation, Fornberg-Whitham equation is reduced to an ordinary differential equation whose general solution can be obtained using the factorization technique. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtain the classification of(More)