Abstract
With the help of the auxiliary function method, we solved the improved Boussinesq (IBq) equation with fluid dynamic damping and the modified IBq (IMBq) equation with Stokes damping, and we obtained their three types of travelling wave exact solutions, which is an extension service of the numerical simulation and the existence of a solution. From the waveform diagram of IBq equation with hydrodynamic damping, it can be seen that when the propagation velocity of kink wave changes, the amplitude also changes significantly, and it is also found that the kink isolated waveform is significantly asymmetric due to the increase of damping coefficient v, which may be of some value in explaining some physical phenomena. In addition, the symbolic computing software maple makes our computing work easier.
Highlights
With the help of the auxiliary function method, we solved the improved Boussinesq (IBq) equation with fluid dynamic damping and the modified IBq (IMBq) equation with Stokes damping, and we obtained their three types of travelling wave exact solutions, which is an extension service of the numerical simulation and the existence of a solution
From the waveform diagram of IBq equation with hydrodynamic damping, it can be seen that when the propagation velocity of kink wave changes, the amplitude changes significantly, and it is found that the kink isolated waveform is significantly asymmetric due to the increase of damping coefficient v, which may be of some value in explaining some physical phenomena
Introduction ere are various kinds of nonlinear phenomena in nature, most of which can be described by nonlinear evolution equations
Summary
Exact Solutions of Damped Improved Boussinesq Equations by Extended (G9/G)-Expansion Method. With the help of the auxiliary function method, we solved the improved Boussinesq (IBq) equation with fluid dynamic damping and the modified IBq (IMBq) equation with Stokes damping, and we obtained their three types of travelling wave exact solutions, which is an extension service of the numerical simulation and the existence of a solution. E IBq equation with hydrodynamic damping term and the IMBq equation with Stokes damping term are obtained, respectively, under the conditions of the third and fourth anharmonic potentials. Naranmandula [15] obtained an equation similar to (4) when studying the propagation of one-dimensional longitudinal wave in nonlinear microstructural solid and simulated the influence of microstructural effect on the evolution of kinked isolated wave by finite difference method: utt − uxx − uxxtt − vuxxt u2xx,. Some of the different approaches are equivalent [41, 42]
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