Analytical approximation of solitary waves with compact support for fractional nonlinear dispersive k(m,n) equations
The study of solitons and compactions plays a crucial role in nonlinear physics. In this paper, we introduce the Multistep Modified Reduced Differential Transform Method (MMRDTM), which integrates Adomian polynomials with a multistep approach. This novel technique efficiently generates analytical ap...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | en |
| Published: |
Semarak Ilmu Publishing
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| Subjects: | |
| Online Access: | https://eprints.ums.edu.my/id/eprint/45555/1/FULLTEXT.pdf https://eprints.ums.edu.my/id/eprint/45555/ |
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| Summary: | The study of solitons and compactions plays a crucial role in nonlinear physics. In this paper, we introduce the Multistep Modified Reduced Differential Transform Method (MMRDTM), which integrates Adomian polynomials with a multistep approach. This novel technique efficiently generates analytical approximations in a rapidly converging sequence while requiring fewer computed terms. By modifying the Reduced Differential Transformation Method (RDTM) and incorporating Adomian polynomials to handle nonlinear terms, the MMRDTM simplifies the solution process for nonlinear initial value problems with reduced computational effort. Furthermore, the multistep approach extends the solution’s convergence over a wider time domain. To validate the effectiveness of MMRDTM, we apply the method in two examples of fractional nonlinear Kortewegde Vries equations (fNKdVEs) with compaction solutions. Graphical representations illustrate the precision and reliability of the technique. The results confirm that the MMRDTM can achieve better approximations to exact solutions efficiently. |
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