In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...

We consider a degenerate parabolic equation with logistic periodic sources. First, we establish the existence of nontrivial nonnegative periodic solutions by monotonicity method. Then by using Moser iterative technique and the method of contradiction, we establish the boundedness estimate of nonnegative periodic solutions, by which we show that the attraction of nontrivial nonnegative periodic ...

We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...

The periodic soliton resonances and recurrent wave solutions to the Davey–Stewartson equation are presented. The solutions that described the interaction between a y-periodic soliton and a line soliton are analyzed to show the existence of the soliton resonances. The various recurrent solutions (The growing-and-decaying mode, breather and rational growing-anddecaying mode solutions) are present...

We consider the bifurcation of periodic solutions from an equilibrium point of the given equation: x =F(x,?) , where x ? R , ? is a vector of real parameters ? , ? , ... , ? and F:R x R ->R has at least second continuous derivations in variables

The stability of periodic solutions of partial differential equations has been an area of increasing interest in the last decade. The KdV equation is known to have large families of periodic solutions that are parameterized by hyperelliptic Riemann surfaces. They are generalizations of the famous multi-soliton solutions. We show that all such periodic solutions are orbitally stable with respect...

New exact solutions with built-in arbitrary functions for the (n + 1)-dimensional double sine-Gordon equation are studied by means of auxiliary solutions of the cubic nonlinear Klein–Gordon (CNKG) fields. By a proper selection of the arbitrary functions and the appropriate solutions of the CNKG systems, new solutions including periodic-solitoffs, periodic-twisted kinks, quasi-periodic and non-p...

After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we discuss a four-dimensional relaxation oscillation and also canard-like solutions emerging from the mo...