Exact solitary wave solutions of the Kadomtsov–Petviashvili–Benjamin–Bona–Mahony equation

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

“…This gives rise to a group invariant solution = ( ) and consequently using these invariants, (5) is transformed into the fourth-order nonlinear ODE…”

“…The solutions of (1) have been studied in various aspects. See, for example, the recent papers [2][3][4][5]. Wazwaz [2,3] used the sine-cosine method, the tanh method and the extended tanh method for finding solitonary solutions of this equation.…”

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

“…The study of nonlinear evolution equations (NLEEs) has been going on for quite a few decades now [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. There has been several improvements that are noticed.…”

Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation

“…Some methods are developed and applied to find exact solutions of nonlinear evolution equations because exact solutions play an important role in the comprehension of nonlinear phenomena. For instance, extended tanh method, extended mapping method with symbol computation, and bifurcation method of dynamical systems are employed to study (3) [4][5][6], and some solitary wave solutions and triangle periodic wave solutions were obtained. However, there is no method which can be applied to all nonlinear evolution equations.…”

“…The purpose of this paper is to apply the bifurcation method [7][8][9][10] of dynamical systems to continue to seek traveling waves of (3). Firstly, we obtain bell-shaped solitary wave solutions involving more free parameters, and some results in [6] are corrected and improved. Then, we get some new periodic wave solutions in parameter forms of Jacobian elliptic function, and numerical simulation verifies the validity of these periodic solutions.…”