Numerical study of fractional model of multi-dimensional dispersive partial differential equation by Vijay Verma, Amit Prakash, Devendra Kumar, Jagdev Singh

“…This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multi-dimensional space. …”
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Analytical Analysis of Fractional-Order Multi-Dimensional Dispersive Partial Differential Equations by Shuang-Shuang Zhou, Mounirah Areshi, Praveen Agarwal, Nehad Ali Shah, Jae Dong Chung, Kamsing Nonlaopon

“…In this paper, a novel technique called the Elzaki decomposition method has been using to solve fractional-order multi-dimensional dispersive partial differential equations. Elzaki decomposition method results for both integer and fractional orders are achieved in series form, providing a higher convergence rate to the suggested technique. …”
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Semi-analytical solutions of the 3rd order fuzzy dispersive partial differential equations under fractional operators by Shabir Ahmad, Aman Ullah, Ali Akgül, Thabet Abdeljawad

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Solution of Fractional Third-Order Dispersive Partial Differential Equations and Symmetric KdV via Sumudu–Generalized Laplace Transform Decomposition by Hassan Eltayeb, Reem K. Alhefthi

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nZVI Mobility and Transport: Laboratory Test and Numerical Model by Paolo Viotti, Giuseppe Sappa, Fabio Tatti, Francesca Andrei

Subjects: “…modified advection-dispersion partial differential equation…”
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Kink and anti-kink wave solutions for the generalized KdV equation with Fisher-type nonlinearity by Huseyin Kocak

“…The proposed equation is a third-order dispersive partial differential equation combining the purely nonlinear convective term with the purely nonlinear reactive term. …”
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Quantum Hasimoto transformation and nonlinear waves on a superfluid vortex filament under the quantum local induction approximation by Van Gorder, R

“…In the present paper, the quantum form of the LIA (which includes mutual friction effects) is put into correspondence with a type of complex nonlinear dispersive partial differential equation (PDE) with cubic nonlinearity (similar in form to a Ginsburg-Landau equation, with additional nonlinear terms). …”

An Efficient Technique of Fractional-Order Physical Models Involving <i>ρ</i>-Laplace Transform by Nehad Ali Shah, Ioannis Dassios, Essam R. El-Zahar, Jae Dong Chung

“…Four numerical problems involving fractional-order third-order dispersive partial differential equations are presented with their analytical solutions. …”
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Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations by Rasool Shah, Hassan Khan, Muhammad Arif, Poom Kumam

“…In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace&#8211;Adomian decomposition method. …”
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Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces by Eiji Onodera

“…We also discuss the relationship between our reduction and the theory of linear dispersive partial differential equations.…”
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Well-posedness of one-dimensional Korteweg models by Sylvie Benzoni-Gavage, Raphael Danchin, Stephane Descombes

“…The resulting equations for the density and the velocity, consisting of the mass conservation law and the momentum conservation with Korteweg stress, are a system of third order nonlinear dispersive partial differential equations. Additionally, this system is Hamiltonian and admits travelling solutions, representing propagating phase boundaries with internal structure. …”
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Physical properties for bidirectional wave solutions to a generalized fifth-order equation with third-order time-dispersion term by Marwan Alquran

“…Higher-order temporal-dispersion partial differential equations have its capability to visualize the evolution of steeper-waves for shorter wave-length better than the higher-order KdV does. …”
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Classical and Multisymplectic Schemes for Linearized KdV Equation: Numerical Results and Dispersion Analysis by Adebayo Abiodun Aderogba, Appanah Rao Appadu

“…This is one of the rare papers that analyse dispersive properties of methods for dispersive partial differential equations. The performance of the schemes are gauged over short and long propagation times. …”
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The role of smoothing effect in some dispersive equations by Grande Izquierdo, Ricardo.

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