[PDF] Top 20 Closed Form Wave Solutions to the Nonlinear Partial Differential Equations via the Rational Expansion Method

... Nonlinear partial differential equations (NPDEs) are widely used to describe complex phenomena in various fields including either the scientific works or engineering fields, such as fluid ... See full document

... - expansion method for constructing exact travelling wave solutions of nonlinear par- tial differential ...selected equations, the balance numbers of which are not ... See full document

... proposed method gives more general exact solutions for four different types of nonlinear partial differential equations such as the modified regularized long wave ... See full document

... Nonlinear partial differential equations (NLPDEs) have a significant role in several scientific and engineering ...These equations appear in con- densed matter, solid state physics, ... See full document

... transformation wave, some nonlinear partial differential equations have been converted into an ...series method for equations with similar linear part, the researchers ... See full document

... scattering method [1], Backlund trans- formation method [11], Darboux Transformations [10], tanh-function method [18], Exp-function method [9] and so .../G)- expansion method ... See full document

... -expansion method with second order linear ordinary differential equation is imple- mented to investigate the fourth order Boussinesq equa- tion involving ...obtained solutions are presented ... See full document

... with nonlinear partial differential equations (PDEs), many methods have been de- ...polynomial method has been proposed by Liu [1]-[5]. By Liu’s method, we can obtain the ... See full document

... travelling wave solutions for nonlinear partial differential equations plays an important role in the study of nonlinear physical ...phenomena. Nonlinear ... See full document

... exact solutions of (1.1) with δ = 0 via quasisolutions of the form Φ(F(x) ...organized method of differential-stäcked matrices in [5] has some advantages over the ad hoc method of [7], ... See full document

... the solutions can be uniformly expressed in terms of some special ...original partial differential equations (PDE’s) can be transformed into a set of algebraic equations through ... See full document

... a nonlinear function, and f x t ( , ) is a known analytic ...of nonlinear partial differential equations such as the Adomian Decomposition Method (ADM) [4-7], the EXP function ... See full document

... /G)-expansion method is used to search for the exact traveling wave solutions of the coupled KdV-mKdV ...function solutions are obtained. It is shown that the method is ... See full document

... equation method has been successfully used to find the exact traveling wave solutions of Kuramoto-Sivashinsky ...The solutions are verified to check the correctness of the solutions by ... See full document

... the equations yield the same solution in the sense of entropy-satisfying weak ...classical solutions nevertheless have shock waves moving at different speeds for the same left and right states ...yield ... See full document

... u + α uu − vu = β u − u u − γ (83) where u is the concentration or density, c represents the convective velocity, and α , β , γ are real constants in different contexts. In which v plays the role of diffusion-like ... See full document

... -expansion method has been extended to solve the nonlinear partial differential equation of frac- tional order, in the sense of modified Riemann-Liouville ...fractional equations ... See full document

... Chromatographic process started from the boundary, and there were many types of the boundary conditions, such as the methods of δ-pulse, wide pulse, head-on, etc; whose corresponding boundary condition was not zero. ... See full document

... proposed method. In section 3, we apply the reduced differential transform method to solve three test examples in order to show its ability and ... See full document

... iteration method, which is a modified general Lagrange multiplier method [34] has been shown to solve effectively, easily and accurately, a large class of nonlinear problems with approximations which ... See full document