Abstract
This article presents the new exact traveling wave solutions of fourth order (1+1)-dimensional Boussinesq equation. We proposed a new exponential expansion method and apply to undertake this study. The analytical solutions are defined by various types of mathematical functions. This study further shows some solitary and periodic waves graphically. This paper also shows that the novel exponential expansion method is easily applicable and powerful mathematical tool in the symbolic computational approach in the field of mathematical physics and engineering. The exact solutions of this equation play a vital role for describing different types of wave propagation in any varied natural instances, especially in water wave dynamics.
Highlights
The nonlinear partial differential equations (NPDEs) are broadly used as models for describing various types of physical mechanisms of natural phenomena in the field of applied sciences and engineering, especially in plasma physics, elastic media, optical fibers, fluid dynamics, quantum mechanics, chimerical physics, biotechnology, signal processing, solid state physics, shallow water wave theory etc
The fourth order (1+1)-dimensional Boussinesq equation is an important class of NPDEs, which was first introduced by Boussinesq to examine the propagation of long waves in shallow water under the gravity propagating in positive and negative directions [27]
We have proposed a new exponential expansion method for solving NPDEs and successfully applied to obtain more explicit and exact traveling wave solutions of the fourth order Boussinesq equation
Summary
The nonlinear partial differential equations (NPDEs) are broadly used as models for describing various types of physical mechanisms of natural phenomena in the field of applied sciences and engineering, especially in plasma physics, elastic media, optical fibers, fluid dynamics, quantum mechanics, chimerical physics, biotechnology, signal processing, solid state physics, shallow water wave theory etc. The fourth order (1+1)-dimensional Boussinesq equation is an important class of NPDEs, which was first introduced by Boussinesq to examine the propagation of long waves in shallow water under the gravity propagating in positive and negative directions [27]. This equation appeared as a model equation to describe the propagation of many other physical phenomena, such as iron sound wave in plasma, nonlinear lattice waves and vibrations in a nonlinear string. Yildrim and Mohud-Din have been applied the He’s semiinverse method to obtain the soliton solution of good
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