New wave patterns to the doubly dispersive equation in nonlinear dynamic elasticity

Pramana ◽  
2020 ◽  
Vol 94 (1) ◽  
Author(s):  
Gulnur Yel
Keyword(s):  
Nonlinear Dynamic ◽  
New Wave ◽  
Dispersive Equation ◽  
Dynamic Elasticity ◽  
Wave Patterns

scholarly journals Regarding New Wave Patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 341 ◽  
Author(s):  
Juan Luis García Guirao ◽  
Haci Mehmet Baskonus ◽  
Ajay Kumar
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Bright Soliton ◽  
New Wave ◽  
Wave Patterns

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.

scholarly journals Novel Soliton Molecules and Wave Interactions for A (3+1)-Dimensional Nonlinear Evolutionary Equation

2021 ◽  
Author(s):  
Xiaoyan Tang ◽  
Chao Jie Cui ◽  
Zu feng Liang ◽  
Wei Ding
Keyword(s):  
Nonlinear Evolution ◽  
Evolutionary Equation ◽  
New Wave ◽  
Variable Separation ◽  
Wave Interactions ◽  
Elastic Interactions ◽  
Localized Excitations ◽  
Soliton Lattice ◽  
Wave Patterns ◽  
Nonlinear Evolutionary Equation

Abstract New wave excitations are revealed for a (3+1)-dimensional nonlinear evolution equation to enrich nonlinear wave patterns in nonlinear systems. Based on a new variable separation solution with two arbitrary variable separated functions obtained by means of the multilinear variable separation approach, localized excitations of N dromions, N x M lump lattice and N x M ring soliton lattice are explored. Interestingly, it is observed that soliton molecules can be composed of diverse "atoms" such as the dromions, lumps and ring solitons, respectively. Elastic interactions between solitons and soliton molecules are graphically demonstrated.

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