Abstract
The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method) can be used to solve other similar nonlinear wave equations.
Highlights
Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of sciences such as biology, chemistry, communication, and especially many branches of physics like condensed matter physics, field theory, fluid dynamics, plasma physics, and optics, and so forth
The more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods can be used to solve other similar nonlinear wave equations
The dynamics of shallow water waves, which are seen in various places like sea beaches, lakes, and rivers, are governed by the Boussinesq equation
Summary
Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of sciences such as biology, chemistry, communication, and especially many branches of physics like condensed matter physics, field theory, fluid dynamics, plasma physics, and optics, and so forth. In recent years there has been much interest in some variants of the Boussinesq systems [2,3,4,5,6] These coupled Boussinesq equations [7] arise in shallow water waves for two-layered fluid flow. The longitudinal wave equation of a finite deformation elastic circular rod, Boussinesq equations, and dispersive long wave equations are nonlinear partial differential equations of different scientific field. We find that they have the same characteristics. The analytical solutions of the differential equations for the elastic circular rod, Boussinesq equations, and dispersive long wave equations are solved by using homogeneous balance method, Jacobi elliptic function method, fixed point method, and modified mapping method. The more physical specifications of these nonlinear equations have been identified and the results indicated
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
