Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method

Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme

New exact travelling wave solutions of generalised sinh- Gordon and (2 + 1)-dimensional ZK-BBM equations

Exact travelling wave solutions have been established for generalised sinh-Gordon andgeneralised (2+1) dimensional ZK-BBM equations by using GG      expansion method whereG  G( ) satisfies a second-order linear ordinary differential equation. The travelling wave solutionsare expressed by hyperbolic, trigonometric and rational functions

Applying Differential Transform Method to Nonlinear Partial Differential Equations: A Modified Approach

This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions

New Soliton Solutions for Systems of Nonlinear Evolution Equations by the Rational Sine-Cosine Method

In this paper, we construct new solitary solutions to nonlinear PDEs by the rational Sine and Cosine method. Moreover, the periodic solutions and bell-shaped solitons solutions to the Benjamin-Bona-Mahony and the Gardner equations are obtained. New solutions to Broer-Kaup (BK) system are also obtained. Finally, the solution of a two-component evolutionary system of a homogeneous Kdv equations of order  has been investigated by the proposed method

Soliton solution and bifurcation analysis of the KP–Benjamin–Bona–Mahoney equation with power law nonlinearity

This paper studies the Kadomtsev–Petviashvili–Benjamin–Bona–Mahoney equation with power law nonlinearity. The traveling wave solution reveals a non-topological soliton solution with a couple of constraint conditions. Subsequently, the dynamical system approach and the bifurcation analysis also reveals other types of solutions with their corresponding restrictions in place

Exact closed form solutions of compound Kdv Burgers’ equation by using generalized (Gʹ/G) expansion method

In this investigation, the compound Korteweg-de Vries (Kd-V) Burgers equation with constant coefficients is considered as the model, which is used to describe the properties of ion-acoustic waves in plasma physics, and also applied for long wave propagation in nonlinear media with dispersion and dissipation. The aim of this paper to achieve the closed and dynamic closed form solutions of the compound KdV Burgers equation. We derived the completely new solutions to the considered model using the generalized (Gʹ/G)-expansion method. The newly obtained solutions are in form of hyperbolic and trigonometric functions, and rational function solutions with inverse terms of the trigonometric, hyperbolic functions. The dynamical representations of the obtained solutions are shown as the annihilation of three-dimensional shock waves, periodic waves, and multisoliton through their three dimensional and contour plots. The obtained solutions are also compared with previously exiting solutions with both analytically and numerically, and found that our results are preferable acceptable compared to the previous results.Publisher's Versio

New Explicit Solutions for Homogeneous Kdv Equations of Third Order by Trigonometric and Hyperbolic Function Methods

In this paper, we study two-component evolutionary systems of the homogeneous KdV equation of the third order types (I) and (II). Trigonometric and hyperbolic function methods such as the sine-cosine method, the rational sine-cosine method, the rational sinh-cosh method, sech-csch method and rational tanh-coth method are used for analytical treatment of these systems. These methods, have the advantage of reducing the nonlinear problem to a system of algebraic equations that can be solved by computerized packages

Exact Solutions and Conservation Laws of a (2+1)-Dimensional Nonlinear KP-BBM Equation

In this paper, we study the two-dimensional nonlinear Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony (KP-BBM) equation. This equation is the Benjamin-Bona-Mahony equation formulated in the KP sense. We first obtain exact solutions of this equation using the Lie group analysis and the simplest equation method. The solutions obtained are solitary waves. In addition, the conservation laws for the KP-BBM equation are constructed by using the multiplier method