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M lump and interaction between M lump and N stripe for the third-order evolution equation arising in the shallow water
- Source :
- Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-20 (2020)
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper, we use the Hirota bilinear method for investigating the third-order evolution equation to determining the soliton-type solutions. The M lump solutions along with different types of graphs including contour, density, and three- and two-dimensional plots have been made. Moreover, the interaction between 1-lump and two stripe solutions and the interaction between 2-lump and one stripe solutions with finding more general rational exact soliton wave solutions of the third-order evaluation equation are obtained. We give the theorem along with the proof for the considered problem. The existence criteria of these solitons in the unidirectional propagation of long waves over shallow water are also demonstrated. Various arbitrary constants obtained in the solutions help us to discuss the graphical behavior of solutions and also grants flexibility in formulating solutions that can be linked with a large variety of physical phenomena. We further show that the assigned method is general, efficient, straightforward, and powerful and can be exerted to establish exact solutions of diverse kinds of fractional equations originated in mathematical physics and engineering. We have depicted the figures of the evaluated solutions to interpret the physical phenomena.
- Subjects :
- Algebra and Number Theory
Partial differential equation
Interaction
Hirota bilinear method
lcsh:Mathematics
Applied Mathematics
Mathematical analysis
The unidirectional propagation
Bilinear interpolation
lcsh:QA1-939
01 natural sciences
Third-order evolution equation
Waves and shallow water
Third order
Ordinary differential equation
0103 physical sciences
Evolution equation
Kondratiev wave
M-lump solutions
The existence criteria
Variety (universal algebra)
010306 general physics
010301 acoustics
Analysis
Mathematics
Subjects
Details
- ISSN :
- 16871847
- Volume :
- 2020
- Database :
- OpenAIRE
- Journal :
- Advances in Difference Equations
- Accession number :
- edsair.doi.dedup.....bae2efa87f42d09c9b5f635fbb1e8618
- Full Text :
- https://doi.org/10.1186/s13662-020-02669-y