Abstract
A Shallow Water Wave-like nonlinear differential equation is considered by using the generalized bilinear equation with the generalized bilinear derivatives D3,x and D3,t, which possesses the same bilinear form as the standard shallow water wave bilinear equation. By symbolic computation, four presented classes of rational solutions contain all rational solutions to the resulting Shallow Water Wave-like equation, which generated from a search for polynomial solutions to the corresponding generalized bilinear equation.
Highlights
In recent years, numerous scientists committed to the research of water waves, the shallow water wave can describe the freedom of the shallow surface under the gravitational influence of one-way transmission, and produce on the bottom of the deep sea
Four presented classes of rational solutions contain all rational solutions to the resulting Shallow Water Wave-like equation, which generated from a search for polynomial solutions to the corresponding generalized bilinear equation
We introduce a Shallow Water Wave (SWW)-like nonlinear differential equation in terms of a generalized bilinear differential equation of Shallow Water Wave type using three generalized bilinear differential operators D3,x and D3,t
Summary
Numerous scientists committed to the research of water waves, the shallow water wave can describe the freedom of the shallow surface under the gravitational influence of one-way transmission, and produce on the bottom of the deep sea. Wronskian formulation or the Casoratian formulation ([2]-[6]) usually deal with integrable equations to find their rational solutions in the literature, such as KdV, Boussinesq, KP, Schrodinger Toda equations and Shallow water wave equ-. Increasingly nonlinear differential equations are studied through the generalized bilinear equation with the generalized bilinear derivatives, for examples, KdV-like equation [12], Boussinesq-like equation [13] and KP-like equation [14]. We introduce a Shallow Water Wave (SWW)-like nonlinear differential equation in terms of a generalized bilinear differential equation of Shallow Water Wave type using three generalized bilinear differential operators D3,x and D3,t. We will search for polynomial solutions to the corresponding generalized bilinear equation by Maple symbolic computation and generate four classes of rational solutions to the resulting Shallow Water Wave-like equation. Four particular rational solutions will be plotted to exhibit different distributions of singularities
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
