A novel optimization-based physics-informed neural network scheme for solving fractional differential equations

M, Sivalingam S; Kumar, Pushpendra; Govindaraj, V.

doi:10.1007/s00366-023-01830-x

Cited by 14 publications

(2 citation statements)

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“…This branch of research is valuable for helping scientists comprehend complex physical phenomena. There are a large number of methods for obtaining exact solutions of nonlinear evolution Equations [13][14][15][16][17][18][19][20]. In [13], the dynamical systems method was proposed for the modified Zakharov equations with a quantum correction.…”

Section: Introductionmentioning

confidence: 99%

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Exact Periodic Wave Solutions for the Perturbed Boussinesq Equation with Power Law Nonlinearity

Kong,

Geng

2024

Mathematics

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In this paper, exact periodic wave solutions for the perturbed Boussinesq equation with power law nonlinearity are obtained for different nonlinear strengths n. When n=1, the periodic traveling wave solutions can be found by the definition of the Jacobian elliptic function. When n≥1, we construct a transformation to solve for the power law nonlinearity, and the periodic traveling wave solutions can be obtained by applying the extended trial equation method. In addition, we consider the limiting case where the periodicity of the periodic traveling wave solutions vanishes, and we obtain the soliton solution for n=1. Numerical simulations show the periodicity of the solution for the perturbed Boussinesq equation.

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Section: Introductionmentioning

confidence: 99%

“…The authors obtained the exact solutions of the nonlinear evolution equation utilizing the B äcklund method [18]. Sivalingam et al studied the fractional differential equations by the neural network scheme in [19,20].…”

Section: Introductionmentioning

confidence: 99%