New Multiple Solution to the Boussinesq Equation and the Burgers-Like Equation

In recent years, nonlinear phenomena play a crucial role in appliedmathematics and physics. Directly searching for exact solutions of nonlinear partial differential equations (PDEs) has become more and more attractive partly due to the availability of computer symbolic systems like Mathematica or Maple that allow us to perform some complicated and tedious algebraic calculation on a computer as well as help us to find exact solutions of PDEs [1–5] now. Many explicit exact methods have been introduced in the literature [6–14]. Some of them are Painlevé method, homogeneous balance method, similarity reduction method, sinecosine method, Darboux transformation, Cole-Hopf transformation, generalized Miura transformation, tanh method, Backlund transformation, and others methods [15, 16]. One of themost effectively straightforwardmethods constructing exact solution of PDEs is the extended tanh function method [17]. Let us simply describe the tanh function. For doing this, one can consider in two variables general form of nonlinear PDE as follows: