| Citation: |
Muhammad Ramzan, Yu-Ming Chu, Hamood ur Rehman, Muhammad Shoaib Saleem, Choonkil Park. SOLITON SOLUTIONS FOR ANTI-CUBIC NONLINEARITY USING THREE ANALYTICAL APPROACHES[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2177-2192. doi: 10.11948/20200380
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SOLITON SOLUTIONS FOR ANTI-CUBIC NONLINEARITY USING THREE ANALYTICAL APPROACHES
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Abstract
In this article, three constructive techniques namely, Expa-function method, the modified Kudryashov method and the generalized tanh-method are adopted to analyze the nonlinear Schrödinger equation having anti-cubic nonlinearity. Nonlinear Schrödinger equation is a comprehensive model that governs wave behavior in optical fiber. Cubic-quintic nonlinear Schrödinger equation, additionally having anti-cubic nonlinear term is investigated to construct bright, dark, kink and singular soliton solutions. The graphical representations of the soliton propagation are also demonstrated by the solutions obtained using these three techniques.
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References
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Muhammad Ramzan, Yu-Ming Chu, Hamood ur Rehman, Muhammad Shoaib Saleem, Choonkil Park. SOLITON SOLUTIONS FOR ANTI-CUBIC NONLINEARITY USING THREE ANALYTICAL APPROACHES[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2177-2192. doi: 10.11948/20200380
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Figure 1. (a) 3-D plot of solution (5.4) for
$ -20\leq x \leq20 $ and$ -5 \leq t\leq10 $ (b) 2-D plot of solution (5.4) for$ x = 0 $ and$ -5 \leq t\leq10 $ -
Figure 2. (a) 3-D plot of solution (5.8) for
$ -10\leq x \leq10 $ and$ -10 \leq t\leq10 $ (b) 2-D plot of solution (5.8) for$ -10 \leq x\leq10 $ and$ t = 0 $ -
Figure 3. (a) 3-D plot of solution (5.12) for
$ -10\leq x \leq10 $ and$ -1 \leq t\leq1 $ (b) 2-D plot of solution (5.12) for$ x = 0 $ and$ -1\leq t \leq1 $ -
Figure 4. (a) 3-D plot of solution (5.13) for
$ -6\leq x \leq6 $ and$ -3 \leq t\leq3 $ (b) 2-D plot of solution (5.13) for$ x = 0 $ and$ -3\leq t \leq3 $ -
Figure 5. (a) 3D plot of solution (5.14) for
$ -6\leq x \leq6 $ and$ -3 \leq t\leq3 $ (b) 2D plot of solution (5.14) for$ x = 0 $ and$ -3\leq t \leq3 $ -
Figure 6. (a) 3D plot of solution (5.15) for
$ -1\leq x \leq0 $ and$ -1 \leq t\leq1 $ (b) 2D plot of solution (5.15) for$ x = 0 $ and$ -1\leq t \leq1 $ -
Figure 7. (a) 3D plot of solution (5.16) for
$ -2\leq x \leq1 $ and$ -1 \leq t\leq2 $ (b) 2D plot of solution (5.16) for$ -2\leq x \leq1 $ and$ t = 0 $