Solving Benjamin-Bona-Mahony equation by using the sn-ns method and the tanh-coth method

Abstract

Abstract. In this study, we consider the Benjamin Bona Mahony equation which is in the form of ut + ux + uux − uxxt = 0. The sn-ns method and the tanh-coth method have been applied to this equation. And then, exact solutions have been obtained.

The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation

“…The modified equation was proposed to simulate long surface gravity waves with small amplitudes propagating in a 1 + 1 dimension. Many researchers have acquired the exact solutions of Equation (2) by applying many various methods, such as the generalized (G /G)-expansion method [26], (G /G)-expansion method [27], Hirota's bilinear method [28], the Lie group method [29], the exp-function method [30], the tanhcoth method, and the sn-ns method [31]. The stochastic Benjamin-Bona-Mahony equation with beta derivative has not been considered until now.…”

Advantages of the Differential Equations for Solving Problems in Mathematical Physics with Symbolic Computation

“…The wave soliton pulse [6], a significant feature of nonlinearity, shows a perfect equilibrium between nonlinearity and dispersion effects. The first integral method is a powerful solution method was presented by the mathematician [7], where this method is characterized with its strength, with high accuracy and ease of application by relying on the characteristics and advantages of the differential equations as well as mathematical software in finding the exact traveling wave solutions for complex and nonlinear equations that specialized of nonlinear physical phenomena, so was applied to an important type of NLEEs and fractional equations as [8][9][10][11] with compare with other methods, for example the homotopy perturbation method [12], the generalized tanh method [13], homotopy analysis method [14], and several methods [15][16][17][18][19][20][21][22], the first integral method has proven its ability to solve various types of non-linear problems and distinguishes it from other methods by its applicable and the various solitary wave solutions that we obtain by using this method.…”

On different kinds of solutions to simplified modified form of a Camassa-Holm equation

“…where sn represents the Jacobi elliptic sine function. This method can be found in variety of applications, see [13,14]. In 2005, the extended Jacobi elliptic function expansion method was introduced by Zhang [15].…”