Abstract
In this paper, the complete discrimination system method is used to construct the exact traveling wave solutions for fractional coupled Boussinesq equations in the sense of conformable fractional derivatives. As a result, we get the exact traveling wave solutions of fractional coupled Boussinesq equations, which include rational function solutions, Jacobian elliptic function solutions, implicit solutions, hyperbolic function solutions, and trigonometric function solutions. Finally, the obtained solution is compared with the existing literature.
Highlights
The coupled system is composed of two or more differential equations [1,2,3]
In recent years, coupled systems have been widely studied by scholars because they come from physics, chemistry, communication, and engineering [4,5,6,7,8]
Many meaningful methods have been proposed to solve the exact solutions of coupled systems, including Lie symmetry analysis [9], the method of dynamical systems [10, 11], Fan subequation method [12], generalized Jacobi elliptic function expansion method [13], extended modified auxiliary equation mapping method [14], and extended modified auxiliary equation mapping method [15]
Summary
The coupled system is composed of two or more differential equations (include ordinary differential equations, partial differential equations fractional partial differential equations, and stochastic partial differential equations) [1,2,3]. It is a very important class of mathematical and physical equations. Among them, constructing the exact traveling wave solution of this kind of coupled system is a very important topic. Many meaningful methods have been proposed to solve the exact solutions of coupled systems, including Lie symmetry analysis [9], the method of dynamical systems [10, 11], Fan subequation method [12], generalized Jacobi elliptic function expansion method [13], extended modified auxiliary equation mapping method [14], and extended modified auxiliary equation mapping method [15].
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