The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-e...

We survey equilibria and traveling waves of plane Couette flow in small periodic cells at moderate Reynolds number Re, adding in the process eight new equilibrium and two new traveling wave solutions to the four solutions previously known. Bifurcations under changes of Re and spanwise period are examined. These non-trivial solutions can only be computed numerically, but they are 'exact' in the ...

The (constrained) canonical reduction of four-dimensional self-dual Yang–Mills theory to two-dimensional Fitzhugh–Nagumo and the real Newell–Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh–Nagumo and Newell– Whitehead equations. The corresponding gauge potential Al and the ...

Abstract: In this paper, we study the application of the known generalized (G ′ G )-expansion method for seeking more exact travelling solutions solutions and soliton solutions of the Kaup-Kupershmidt equation and the (2+1) dimensional breaking soliton equation. As a result, we come to the conclusion that the traveling wave solutions for the two non-linear equations are obtained in three arbitr...

We present a spectrally accurate numerical method for finding non-trivial timeperiodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the in...

In this paper, a new generalized F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the (2+1)-dimensional dispersive long wave equations to illustrate the validity and advantages of the proposed method. As a result, many new and more general exact non-traveling wave and coefficient function solutions are obtai...

where p,q and r are arbitrary constants. We construct twenty five exact traveling wave solutions of the (1+1)-dimensional modified KdV equation involving parameter by applying this method. The solutions are presented in terms of the hyperbolic, the trigonometric and the rational functional form including solitons and periodic solutions. Moreover, it is worth mentioning that one of our obtained ...

solitary wave solutions to the broer-kaup equations and approximate long water wave equa-tions are considered challenging by using the rst integral method.the exact solutions obtainedduring the present investigation are new. this method can be applied to nonintegrable equa-tions as well as to integrable ones.

differential transform method has been applied to solve many functional equations so far. in this article, we have used this method to solve wave-like equations. differential transform method is capable of reducing the size of computational work. exact solutions can also be achieved by the known forms of the series solutions. some examples are prepared to show theefficiency and simplicity of th...