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Abundant closed-form wave solutions to the simplified modified Camassa-Holm equation

Journal of Ocean Engineering and Science 2023年第3期8卷 238-245页

作者： S M Rayhanul Islam S M Yiasir Arafat Hanfeng Wang School of Civil Engineering Central South UniversityChangshaHunan 410075China Department of Mathematics Pabna University of Science and TechnologyPabna 6600Bangladesh

The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (nae) method has been applied to the SMCH equation. Base on the method, we have obtained some novel an- alytical solutions such as hyperbolic, trigonometric, exponential, and rational function solutions of the SMCH equation. For appropriate values of parameters, three dimensional (3D) and two dimensional (2D) graphs are designed by Mathematica. The stability of the model is also discussed in this manuscript. The dynamic and physical behaviors of the solutions derived from the SMCH equation have been ex- tensively discussed by these plots. All our solutions are indispensable for understanding the nonlinear phenomena of dispersive waves that are important in ocean engineering and science. In addition, our results are essential to clarify the various oceanographic applications containing ocean gravity waves, offshore rig in water, energy associated with a moving ocean wave and numerous other related phenom- ena. Finally, the obtained solutions are helpful for studying wave interactions in many new structures and high-dimensional models.

关键词： SMCH equation nae method Nonlinear physics Kink shape Solitary wave

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