Md. Nur Alam

Some new exact traveling wave solutions to the simplified MCH equation and the (1 + 1)-dimensional combined KdV–mKdV equations

Abstract The generalized (G′/G)-expansion method is thriving in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this paper, we bring to bear the generalized (G′/G)-expansion method to look for the exact solutions via the simplified MCH equation and the (1 + 1)-dimensional combined KdV–mKdV equations involving parameters. When the parameters take special values, solitary wave solutions are originated from the traveling wave solutions. It is established that the generalized (G′/G)-expansion method offers a further influential mathematical tool for constructing the exact solutions of NLEEs in mathematical physics.

Application of the Novel (G′/G)-Expansion Method to the Regularized Long Wave Equation

Abstract In this paper we investigate the regularized long wave equation involving parameters by applying the novel (G′/G)-expansion method together with the generalized Riccati equation. The solutions obtained in this manuscript may be imperative and significant for the explanation of some practical physical phenomena. The performance of this method is reliable, useful, and gives us more new exact solutions than the existing methods such as the basic (G′/G)-expansion method, the extended (G′/G)-expansion method, the improved (G′/G)-expansion method, the generalized and improved (G′/G)-expansion method etc. The obtained traveling wave solutions including solitons and periodic solutions are presented through the hyperbolic, the trigonometric and the rational functions. The method turns out to be a powerful mathematical tool and a step foward towards, albeit easily and yet efficiently, solving nonlinear evolution equations.

An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules

Abstract In this article, a variety of solitary wave solutions are observed for microtubules (MTs). We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs) involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method.

A novel G′/G-expansion method for solving the 3 + 1-dimensional modified KdV-Zakharov-Kuznetsov equation in mathematical physics

A novel G′/G-expansion method is presented in this article to construct more general type and new travelling wave solutions of non-linear evolution equations. The method is illustrated in its application via the 3 + 1-dimensional modified KdV-Zakharov-Kuznetsov equation which is used to model different non-linear phenomena. Through the assistance of Maple, we obtain several new and more general travelling wave solutions in terms of the hyperbolic functions, the trigonometric functions, the rational functions and their combination with parameters. The solutions obtained in this article can successfully recover previously known solutions by setting particular values of the parameters that have been found by other sophisticated methods.

Application of Exp(())-expansion Method to Find the Exact Solutions of Nonlinear Evolution Equations

In this paper, we explore new applications of the )) ( exp(    -expansion method for finding exact traveling wave solutions of generalized Klein-Gordon Equation and right-handed nc-Burgers equation. By means of this method three new solutions of each equations is obtained including the hyperbolic functions, exponential functions and rational function solutions. The proposed method is very effective, efficient and applicable mathematical tools for nonlinear evolution equations (NLEEs). So this method can be used for many other nonlinear evolution equations.

A Note on Novel ( G'/G) -expansion Method in Nonlinear Physics

Abstract: The exact solutions of nonlinear evolution equations (NLEEs) play a critical role to make known the internal mechanism of complex physical phenomena. In this article, we construct the traveling wave solutions of the (1+1)-dimensional KdV equation and the Banjamin-Ono equation by means of the novel (G0/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric and rational functions. It is shown that the novel (G0/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.