| Citation: |
Parvaiz Ahmad Naik, Manzoor Ahmad, Dowlath Fathima, Akbar Zada. EXPLORING THE IMPACT OF MULTIPLICATIVE NOISE ON THE SOLITON DYNAMICS IN THE FRACTIONAL BREAKING SOLITON EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1756-1783. doi: 10.11948/20250259
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EXPLORING THE IMPACT OF MULTIPLICATIVE NOISE ON THE SOLITON DYNAMICS IN THE FRACTIONAL BREAKING SOLITON EQUATION
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Abstract
This paper investigates the fractional space-time stochastic $ (2+1) $-dimensional breaking soliton equation $ (\mathrm{FSTSBSE}) $ using the $ M $-truncated fractional derivative. We apply the Generalized Kudryashov-Auxiliary-Jacobian Method (GKAJM) to obtain exact solutions of the $ \mathrm{FSTSBSE} $. Several classes of analytical solutions, including trigonometric and hyperbolic forms, are derived. The solutions presented in this study extend and generalize various results previously reported in the literature. Moreover, Maple is employed to generate contour and three-dimensional plots of the obtained fractional-stochastic solutions, providing insight into the influence of multiplicative noise and the $ M $-truncated fractional derivative on the behavior and symmetry of the $ \mathrm{FSTSBSE} $ solutions. In general, the inclusion of a noise term that breaks solution symmetry tends to enhance stability. Since the combination of fractional spatial effects and multiplicative noise via the proposed approach has not previously been applied to this system, earlier related results are treated as special cases within our more general framework.
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References
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Parvaiz Ahmad Naik, Manzoor Ahmad, Dowlath Fathima, Akbar Zada. EXPLORING THE IMPACT OF MULTIPLICATIVE NOISE ON THE SOLITON DYNAMICS IN THE FRACTIONAL BREAKING SOLITON EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1756-1783. doi: 10.11948/20250259
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Figure 1.
The 3D and contour graphs representing
$ |\varphi_{2, 1}(x, y, t)| $ $ m=.999999991 $ $ \sigma_{2}=(1+\iota)^{4} $ $ \beta=1 $ $ \alpha=1 $ $ y=1 $ -
Figure 2.
The 3D and contour graphs representing
$ |\varphi_{2, 5}(x, y, t)| $ $ m=.9999999999999999999999991 $ $ \sigma_{2}=(1+2\iota)^{4} $ $ \beta=1 $ $ \alpha=1 $ $ y=1 $ -
Figure 3.
The 3D graphs representing
$ |\varphi_{2, 8}(x, y, t)| $ $ m=0.00001 $ $ \sigma_{2}=(1+2\iota)^{4} $ $ \beta=1 $ $ \alpha=1 $ $ y=1 $ -
Figure 4.
The 3D and contour graphs representing
$ |\varphi_{2, 10}(x, y, t)| $ $ m=0.1e-11 $ $ \sigma_{2}=(1+2\iota)^{4} $ $ \beta=1 $ $ \alpha=1 $ $ y=1 $ -
Figure 5.
The 3D and contour graphs representing
$ |\varphi_{2, 11}(x, y, t)| $ $ m=.9999999999999991 $ $ S_{-2}=(1-4\iota)^{4} $ $ \beta=1 $ $ \alpha=1 $ $ y=1 $ -
Figure 6.
The 3D and contour graphs representing
$ |\varphi_{2, 12}(x, y, t)| $ $ m=0.1e-16 $ $ \sigma_{2}=(1+4\iota)^{4} $ $ \beta=1 $ $ \alpha=1, \; y=1 $ -
Figure 7.
The 3D and contour graphs representing
$ |\varphi_{2, 17}(x, y, t)| $ $ m=.99999999999999999999991 $ $ \sigma_{2}=(1+2\iota)^{4} $ $ \beta=1 $ $ \alpha=1 $ $ y=1 $ -
Figure 8.
The 3D and contour graphs representing
$ |\varphi_{2, 18}(x, y, t)| $ $ m=0.1e-11 $ $ \sigma_{2}=(1+\iota)^{4} $ $ \beta=1 $ $ \alpha=1 $ $ y=1 $ -
Figure 9.
The 3D and contour graphs representing
$ |\varphi_{2, 20}(x, y, t)| $ $ m=0.1e-11 $ $ \sigma_{2}=(1+\iota)^{4} $ $ \beta=1 $ $ \alpha=1 $ $ y=1 $