In this paper, using modified FF-expansion method, we present some explicit formulas of exact traveling wave solutions for the foam drainage equation. A modified FF-expansion method is proposed by taking full advantages of FF-expansion method and Riccati equation in seeking exact solutions of non-linear partial differential equations.

In this paper, using ( ′ G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation. Keywords—Exact solution, The (3+1)-dimensiona...

Relativistic hydrodynamics can be successfully applied both at the largest and the smallest scales of physics. However, its equations are highly nonlinear, and only few exact relativistic solutions are presently known. We present here a recently found family of exact solutions [1]. These generalize the Landau-Khalatnikov solution [2–4], as they are also accelerating and yield a finite rapidity ...

ABSTRACT In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric ...

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as...

In this work, by using a simple transformation technique, we have show that the nonlinear wave equations: Zakharov equations and generalized Zakharov equations can be reduced to the same family of Duffing or double-well Duffing equations. Then by means of quotient trigonometric function expansion method, many kinds of exact and explicit solutions of this family of equations are obtained in a un...

In this paper, based on a Lax pair of the Riccati form for the general KdV equation, a new auto-Bäcklund transformation (ABT) is presented. As an application of this ABT, since only integration is needed, a series of explicit and exact solutions can be obtained which contain soliton-like solutions. This approach is important for finding more new and physically significant exact solutions of non...

For the first time exact analytical solutions to the eikonal equations in (1+ 1) dimensions with a refractive index being a saturated function of intensity are constructed. It is demonstrated that the solutions exhibit collapse; an explicit analytical expression for the self-focusing position, where the intensity tends to infinity, is found. Based on an approximated Lie symmetry group, solution...

In this Letter, we study (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation by using the new generalized transformation in Homogeneous Balance Method (HBM). As a result, many explicit exact solutions, which contain new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.  2002 Elsevi...